Document:

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                                                                  EXHIBIT 10.1.5

                        [Form of Shareholders Agreement]

                             SHAREHOLDERS AGREEMENT

                                  BY AND AMONG

                                  [_________],

                                  [_________],

                                  [_________],

                                  [_________],

                                  [_________],

                                  [_________],

                                  [_________],

                                  [_________],

                                       AND

                             ARCH CAPITAL GROUP LTD.

                          DATED AS OF [_________], 2001
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                                TABLE OF CONTENTS

                                                                            PAGE

                                    ARTICLE I

                               CERTAIN DEFINITIONS

Section 1.1.   Certain Definitions............................................2

                                   ARTICLE II

                         REPRESENTATIONS AND WARRANTIES

Section 2.1.   Representations and Warranties of the Company..................7
Section 2.2.   Representations and Warranties of Warburg......................7
Section 2.3.   Representations and Warranties of H&F..........................8

                                   ARTICLE III

                          VOTING; BOARD REPRESENTATION

Section 3.1.   Board of Directors.............................................8
Section 3.2.   Committees of the Board.......................................10
Section 3.3.   Investor Protection Matters...................................10
Section 3.4.   Voting........................................................12
Section 3.5.   Chairman of the Company.......................................12
Section 3.6.   Certain Transactions..........................................12

                                   ARTICLE IV

                               REGISTRATION RIGHTS

Section 4.1.   Demand Registrations..........................................13
Section 4.2.   Shelf Registration............................................15
Section 4.3.   Piggy-Back Registration.......................................15
Section 4.4.   Allocation of Shares to be Registered.........................16
Section 4.5.   Registration Procedures.......................................17
Section 4.6.   Registration Expenses.........................................20
Section 4.7.   Indemnification; Contribution.................................20

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                                                                            PAGE

                                    ARTICLE V

            TAG-ALONG RIGHTS; RESTRICTIONS ON TRANSFER AND CONVERSION

Section 5.1.   Tag-Along Rights..............................................23
Section 5.2.   Restrictions on Transfer......................................23
Section 5.3.   Restrictions on Conversion....................................24

                                   ARTICLE VI

                 RESTRICTIONS ON DIVIDENDS AND SHARE REPURCHASES

                                   ARTICLE VII

                          EFFECTIVENESS AND TERMINATION

Section 7.1.   Effectiveness.................................................24
Section 7.2.   Termination...................................................24

                                  ARTICLE VIII

                                  MISCELLANEOUS

Section 8.1.   Injunctive Relief.............................................25
Section 8.2.   Successors and Assigns........................................25
Section 8.3.   Amendments; Waiver............................................25
Section 8.4.   Notices.......................................................26
Section 8.5.   Applicable Law................................................27
Section 8.6.   Headings......................................................27
Section 8.7.   Integration...................................................28
Section 8.8.   Severability..................................................28
Section 8.9.   Consent to Jurisdiction.......................................28
Section 8.10.  Counterparts..................................................28

                                      -ii-
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      SHAREHOLDERS AGREEMENT, dated as of [________], 2001 (this "AGREEMENT"),
by and among ARCH Capital Group Ltd., a company registered under the laws of
Bermuda (the "COMPANY"), [__________], a [__________] organized under the laws
of [__________], [__________], a [__________] organized under the laws of
[__________], [__________], a [__________] organized under the laws of
[__________], [__________], a [__________] organized under the laws of
[__________] (each, a "WARBURG PURCHASER," and collectively, "WARBURG"),
[__________], a [__________] organized under the laws of [__________],
[__________], a [__________] organized under the laws of [__________],
[__________], a [__________] organized under the laws of [__________], and
[__________], a [__________] organized under the laws of [__________] (each, a
"H&F PURCHASER," and collectively, "H&F," and together with Warburg and such
other Persons as may hereafter become parties hereto (solely for purposes of
Article IV and Sections 3.4 and 5.3 hereof) pursuant to the terms of Section 8.2
hereof, the "INVESTORS").

                              W I T N E S S E T H:

      WHEREAS, the Company and the Investors have entered into a Subscription
Agreement, dated as of [________], 2001 (the "SUBSCRIPTION AGREEMENT"), pursuant
to the terms of which, among other things, the Company shall issue and sell to
the Investors, and Investors shall acquire from the Company, (1) Series A
Convertible Preference Shares, par value U.S. $0.01 per share, of the Company
(the "PREFERENCE SHARES"), and (2) Class A Warrants to purchase common shares,
par value U.S. $0.01 per share, of the Company (the "COMMON SHARES") (the "CLASS
A WARRANTS," and together with the Preference Shares, the "PURCHASED
SECURITIES") (such sale and purchase and the other transactions contemplated by
the Subscription Agreement, the "TRANSACTIONS");

      WHEREAS, the execution of this Agreement is a condition to the obligation
of the parties to consummate the Transactions; and

      WHEREAS, the Company and Investors desire to establish in this Agreement
certain terms and conditions concerning the acquisition of Purchased Securities
and related provisions concerning the Investors' relationship with and
investment in the Company following the consummation of the Transactions;

      NOW, THEREFORE, in consideration of the mutual covenants and agreements
set forth herein and for other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the parties hereto hereby agree as
follows:
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                                      -2-

                                    ARTICLE I

                               CERTAIN DEFINITIONS

      Section 1.1. CERTAIN DEFINITIONS. In addition to other terms defined
elsewhere in this Agreement, as used in this Agreement, the following terms
shall have the meanings ascribed to them below:

      "AFFILIATE" shall mean, with respect to any Person, any other Person that
directly, or indirectly through one or more intermediaries, controls, or is
controlled by, or is under common control with, such first Person (including
with respect to individuals, any trusts, foundations, family limited
partnerships or similar entities); PROVIDED, HOWEVER, that no portfolio
investment of either Warburg or H&F, or any of their respective Affiliates,
shall be deemed to be an Affiliate of Warburg or H&F, as the case may be. As
used in this definition, "control" (including, with correlative meanings,
"controlled by" and "under common control with") shall mean possession, directly
or indirectly, of power to direct or cause the direction of management or
policies (whether through ownership of securities or partnership or other
ownership interests, by contract or otherwise).

      "AGREEMENT" shall have the meaning assigned to such term in the preamble
hereto.

      "APPROVAL DATE" shall mean the later of the dates on which the Requisite
Shareholder Approval and the Requisite Regulatory Approval occur.

      "BENEFICIALLY OWN" shall mean, with respect to any securities, having
"beneficial ownership" of such securities for purposes of Rule 13d-3 or 13d-5
under the Exchange Act as in effect on the date hereof, and "BENEFICIAL
OWNERSHIP" shall have the corresponding meaning.

      "BLACKOUT PERIOD" shall have the meaning assigned in Section 4.1(c).

      "BOARD" shall mean the duly elected Board of Directors of the Company in
office at the applicable time.

      "BUSINESS DAY" shall mean any day that is not a Saturday, Sunday or other
day on which the commercial banks in New York City are authorized or required by
law to remain closed.

      "BYE-LAWS" shall mean the bye-laws of the Company.

      "CLAIMS" shall have the meaning assigned in Section 4.7(a).

      "CLASS A WARRANTS" shall have the meaning assigned in the recitals hereto.
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                                      -3-

      "CLOSING" shall mean the consummation of the Transactions pursuant to the
terms of the Subscription Agreement.

      "COMMON SHARES" shall have the meaning assigned in the recitals hereto.

      "COMPANY" shall have the meaning assigned in the preamble hereto.

      "DEMAND REGISTRATION" shall mean any registration effected pursuant to a
Warburg Demand Request or a H&F Demand Request.

      "DIRECTOR" shall mean any member of the Board.

      "EFFECTIVE PERIOD" shall have the meaning assigned in Section 4.5(a)(3).

      "EXCHANGE ACT" shall mean the Securities Exchange Act of 1934, as amended,
and the rules and regulations that may from time to time be promulgated
thereunder.

      "EXISTING REGISTRATION RIGHTS" shall have the meaning assigned in Section
4.1(a) hereof.

      "H&F" shall have the meaning assigned in the preamble hereto.

      "H&F DEMAND REQUEST" shall have the meaning assigned in Section 4.1(b)
hereof.

      "H&F DEMAND SHARES" shall have the meaning assigned in Section 4.1(b)
hereof.

      "H&F DIRECTORS" shall have the meaning assigned in Section 3.1(c) hereof.

      "H&F PURCHASER" shall have the meaning assigned the preamble hereto.

      "H&F REGISTRABLE SHARES" shall have the meaning assigned in Section 4.1(b)
hereof.

      "H&F RETAINED PERCENTAGE" shall mean the quotient, expressed as a
percentage, of (a) the Retained H&F Investment, over (b) the Initial H&F
Investment.

      "INDEPENDENT DIRECTOR" means a Director who is not an Affiliate of
either Warburg or H&F.

      "INITIAL H&F DIRECTOR" shall have the meaning assign in Section 3.1(b).

      "INITIAL H&F INVESTMENT" shall mean, at any time, the product of (a) the
Initial H&F Shares, and (b) the Per Share Price.

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                                      -4-

      "INITIAL H&F SHARES" shall mean (a) the Preference Shares acquired by H&F
at the Closing, (b) any additional Preference Shares acquired by H&F pursuant to
the terms of the Subscription Agreement, (c) any Common Shares acquired by H&F
after the Closing in accordance with terms of the Preference Shares or the Class
A Warrants and (d) any Common Shares or other securities issued in respect the
securities described in clauses (a) though (c) of this definition or into which
securities shall be converted in connection with stock splits, reverse stock
splits, stock dividends or distributions, or combinations or similar
recapitalizations.

      "INITIAL SHARES" shall mean the Initial H&F Shares together with the
Initial Warburg Shares.

      "INITIAL WARBURG DIRECTOR" shall have the meaning assigned in Section
3.1(b) hereof.

      "INITIAL WARBURG INVESTMENT" shall mean, at any time, the product of (a)
the Initial Warburg Shares, and (b) the Per Share Price.

      "INITIAL WARBURG SHARES" shall mean (a) the Preference Shares acquired by
Warburg at the Closing, (b) any additional Preference Shares acquired by Warburg
pursuant to the terms of the Subscription Agreement, (c) any Common Shares
acquired by Warburg after the Closing in accordance with terms of the Preference
Shares or the Class A Warrants and (d) any Common Shares or other securities
issued in respect the securities described in clauses (a) through (c) of this
definition or into which securities shall be converted in connection with stock
splits, reverse stock splits, stock dividends or distributions, or combinations
or similar recapitalizations.

      "INTERESTED PARTY TRANSACTION" shall mean any transaction between the
Company or any of its Subsidiaries and any officer or Director, or Affiliate of
any officer or Director, of the Company.

      "INVESTORS" shall have the meaning assigned in the preamble hereto.

      "INVESTOR SHARES" shall mean, at any time, the Preference Shares, any
additional Preference Shares acquired pursuant to the terms thereof or of the
Subscription Agreement and any Common Shares hereafter acquired by an Investor
after the Closing in accordance with terms of the Preference Shares, the Class A
Warrants or otherwise (and any Common Shares or other securities issued in
respect thereof or into which such Common Shares shall be converted in
connection with stock splits, reverse stock splits, stock dividends or
distributions, or combinations or similar recapitalizations).

      "MANDATORY CONVERSION DATE" shall have the meaning set forth in Section
3.3 hereof.

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                                      -5-

      "MARKET VALUE" shall mean, as of any date, the average of the daily high
and low sales prices per Common Share on the Nasdaq for each of the twenty full
trading days immediately preceding (but not including) such date.

      "MATERIAL TRANSACTION" shall have the meaning assigned in Section 4.1(c).

      "MAXIMUM NUMBER" shall have the meaning assigned in Section 4.4.

      "NASDAQ" shall mean the Nasdaq Stock Market, Inc.

      "NEW ISSUANCE NOTICE" shall have the meaning assigned in Section 5.1
hereof.

      "PARTICIPATING INVESTOR" shall have the meaning assigned in Section
4.5(a)(1) hereof.

      "PERSON" shall mean any individual, corporation, partnership, limited
liability company, association, trust or other entity or organization, including
a government or political subdivision or an agency or instrumentality thereof.

      "PIGGY-BACK REGISTRATION" shall have the meaning assigned in Section 4.3.

      "PIGGY-BACK REQUEST" shall have the meaning assigned in Section 4.3.

      "PER SHARE PRICE" shall have the meaning assigned in the Subscription
Agreement.

      "PREFERENCE SHARES" shall have the meaning assigned in the recitals
hereto.

      "PURCHASED SECURITIES" shall have the meaning assigned in the recitals
hereto.

      "REGISTRABLE SHARES" shall have the meaning assigned in Section 4.1(b)
hereof.

      "REQUISITE REGULATORY APPROVAL" means approval by the applicable insurance
authorities of the acquisition of greater than 9.9% of the Voting Power by
Warburg and H&F.

      "REQUISITE SHAREHOLDER APPROVAL" means the approval by the holders of
Common Shares and Preference Shares of (1) an amendment to paragraphs 45 and 75
of the Bye-laws as contemplated by the Subscription Agreement, and (2) the
issuance of the Common Shares into which the Preference Shares are convertible.

      "RETAINED H&F INVESTMENT" means, at any time, the product of (a) any
Initial H&F Shares Beneficially Owned by H&F at such time, and (b) the Per Share
Price.

      "RETAINED PERCENTAGE" shall mean the H&F Retained Percentage or the
Warburg Retained Percentage, as may be applicable.
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                                      -6-

      "RETAINED WARBURG INVESTMENT" means, at any time, the product of (a) any
Initial Warburg Shares Beneficially Owned by Warburg at such time, and (b) the
Per Share Price.

      "SEC" shall mean the United States Securities and Exchange Commission.

      "SECURITIES ACT" shall mean the Securities Act of 1933, as amended, and
the rules and regulations that may from time to time be promulgated thereunder.

      "SELLING INVESTOR" shall have the meaning assigned in Section 5.2 hereof.

      "SHELF REGISTRATION STATEMENT" shall have the meaning assigned in Section
4.2 hereof.

      "SUBSCRIPTION AGREEMENT" shall have the meaning assigned in the recitals
hereto.

      "SUBSIDIARY" means, with respect to any Person, any other entity of which
securities or other ownership interests having ordinary power to elect a
majority of the board of directors or other persons performing similar functions
are at any time directly or indirectly owned by such Person.

      "TAG-ALONG INVESTOR" shall have the meaning assigned in Section 5.2
hereof.

      "THIRD PARTY SALE" shall have the meaning assigned in Section 5.2 hereof.

      "THIRD PARTY SALE NOTICE" shall have the meaning assigned in Section 5.2
hereof.

      "TRANSACTIONS" shall have the meaning assigned in the recitals hereto.

      "VOTES" shall mean votes entitled to be cast generally in the election of
Directors.

      "VOTING POWER" shall mean, calculated at a particular point in time, the
ratio, expressed as a percentage, of (a) the Votes represented by the Voting
Securities with respect to which the Voting Power is being determined, to (b)
the aggregate Votes represented by all then outstanding Voting Securities. For
this purpose, the votes attributable to the Preference Shares shall be on an
as-converted basis, without regard to the limitations imposed under the
Certificate of Designations.

      "VOTING SECURITIES" shall mean (a) the Common Shares, (b) the Preference
Shares and (c) shares of any other class of securities of the Company then
entitled to vote generally in the election of Directors.

      "WARBURG" shall have the meeting assigned in the preamble hereto.

      "WARBURG DEMAND REQUEST" shall have the meaning assigned in Section 4.1(a)
hereof.
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                                      -7-

      "WARBURG DEMAND SHARES" shall have the meaning assigned in Section 4.1(a)
hereof.

      "WARBURG DIRECTORS" shall have the meaning assigned in Section 3.1(c)
hereof.

      "WARBURG PURCHASER" shall have the meaning assigned in the preamble
hereto.

      "WARBURG REGISTRABLE SHARES" shall have the meaning assigned in Section
4.1(a) hereof.

      "WARBURG RETAINED PERCENTAGE" shall mean the quotient, expressed as a
percentage, of (a) the Retained Warburg Investment, over (b) the Initial Warburg
Investment.

                                   ARTICLE II

                         REPRESENTATIONS AND WARRANTIES

      Section 2.1. REPRESENTATIONS AND WARRANTIES OF THE COMPANY. The Company
represents and warrants to each Investor as follows:

            (a) The Company has been duly formed and is validly existing as a
      company in good standing under the laws of Bermuda and has all necessary
      corporate power and authority to enter into this Agreement and to carry
      out its obligations hereunder.

            (b) This Agreement has been duly and validly authorized by the
      Company and the Company has taken all necessary and appropriate action to
      execute and deliver this Agreement and to perform its obligations
      hereunder.

            (c) This Agreement has been duly executed and delivered by the
      Company and, assuming due authorization and valid execution and delivery
      by each other party hereto, is a valid and binding obligation of the
      Company, enforceable against it in accordance with its terms.

      Section 2.2. REPRESENTATIONS AND WARRANTIES OF WARBURG. Each Warburg
Purchaser represents and warrants to H&F and the Company as follows:

            (a) Such Warburg Purchaser has been duly formed and is validly
      existing and in good standing, to the extent applicable, under the laws of
      its respective jurisdiction of formation and has all necessary corporate
      power and authority to enter into this Agreement and to carry out its
      obligations hereunder.
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                                      -8-

            (b) This Agreement has been duly and validly authorized by such
      Warburg Purchaser and such Warburg Purchaser has taken all necessary and
      appropriate action to execute and deliver this Agreement and to perform
      its obligations hereunder.

            (c) This Agreement has been duly executed and delivered by such
      Warburg Purchaser and, assuming due authorization and valid execution and
      delivery by the Company, is a valid and binding obligation of such Warburg
      Purchaser, enforceable against it in accordance with its terms.

      Section 2.3. REPRESENTATIONS AND WARRANTIES OF H&F. Each H&F Purchaser
represents and warrants to Warburg and the Company as follows:

            (a) Such H&F Purchaser has been duly formed and is validly existing
      under the laws of its respective jurisdiction of formation and has all
      necessary corporate power and authority to enter into this Agreement and
      to carry out its obligations hereunder.

            (b) This Agreement has been duly and validly authorized by such H&F
      Purchaser and such H&F Purchaser has taken all necessary and appropriate
      action to execute and deliver this Agreement and to perform its
      obligations hereunder.

            (c) This Agreement has been duly executed and delivered by such H&F
      Purchaser and, assuming due authorization and valid execution and delivery
      by the Company, is a valid and binding obligation of such H&F Purchaser,
      enforceable against it in accordance with its terms.

                                   ARTICLE III

                          VOTING; BOARD REPRESENTATION

      Section 3.1. BOARD OF DIRECTORS. (a) The Company shall be managed by its
duly elected officers subject to the overall direction and supervision of the
Board. Each of Warburg and H&F shall, and shall cause its controlled Affiliates
to, vote all Voting Securities that such Investor and its controlled Affiliates
Beneficially Own and take any and all actions as may be reasonably necessary to
cause the provisions of this Section 3.1, including the election of the Warburg
Directors and H&F Directors, to be effectuated.

      (b) Prior to the Closing, and as a condition to the Closing, the Company
shall use its best efforts to secure the resignation of a number of Directors
such that there remain only five Directors immediately following the Closing.
Immediately following the Closing, the
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                                      -9-

size of the Board shall be decreased such that the Board shall consist of seven
Directors, and one Director designated by Warburg, (the "INITIAL WARBURG
DIRECTOR") and one Director designated by H&F (the "INITIAL H&F DIRECTOR") shall
each be appointed by the Board as a director to serve in such classes of
Directors as may be necessary to assure that each class in Directors is as near
in equal in number as possible and that the Initial Warburg Director and the
Initial H&F Director are distributed among different classes.

      (c) Effective as of 12:00 a.m. on the date immediately following the
Approval Date, the size of the Board shall be increased such that the Board
shall then consist of 11 Directors and (1) three individuals designated by
Warburg (together with the Initial Warburg Director, and any other replacements
or substitutions therefor, the "WARBURG DIRECTORS") and (2) one individual
designated by H&F (together with the Initial H&F Director, and any other
replacements or substitutions therefor, the "H&F DIRECTORS") shall each be
appointed by the Board as a Director to serve in such classes of Directors as
may be necessary to assure that each class in Directors is as near in equal in
number as possible and that the Warburg Directors and the H&F Directors,
respectively, are distributed among different classes.

      (d) For so long as the Warburg Retained Percentage is equal to or exceeds
75%, the Initial Warburg Director and, following the Approval Date each Warburg
Director, shall be included in the slate of nominees recommended by the Board to
shareholders for election as directors at each annual general meeting of
shareholders at which such Warburg Director's term is scheduled to expire. For
so long as the Warburg Retained Percentage is less than 75% but exceeds or is
equal to 50%, there shall be a number of individuals designated by Warburg
included in the slate of nominees recommended by the Board to shareholders for
election as directors at each annual general meeting of shareholders such that
the aggregate number of Warburg Directors shall be not less than three. For so
long as the Warburg Retained Percentage is less than 50% but exceeds or is equal
to 30%, there shall be a number of individuals designated by Warburg included in
the slate of nominees recommended by the Board to shareholders for election as
directors at each annual general meeting of shareholders such that the aggregate
number of Warburg Directors shall be not less than two. For so long as the
Warburg Retained Percentage is less than 30% but is equal to or exceeds 10%,
there shall be a number of individuals designated by Warburg included in the
slate of nominees recommended by the Board to shareholders for election as
directors at each annual general meeting of shareholders such that the aggregate
number of Warburg Directors shall be not less than one. For so long as Warburg
has the power to have at least one Director included in the slate of nominees
recommended by the Board, such power shall be exercised by Warburg Pincus
Bermuda Private Equity VIII, L.P.

      (e) For so long as the H&F Retained Percentage is equal to or exceeds 60%,
each H&F Director shall be included in the slate of nominees recommended by the
Board to shareholders for election as directors at each annual general meeting
of shareholders at which such
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                                      -10-

H&F Director's term is scheduled to expire. For so long as the H&F Retained
Percentage is less than 60% but is equal to or exceeds 20%, there shall be a
number of individuals designated by H&F included in the slate of nominees
recommended by the Board to shareholders for election as directors at each
annual general meeting of shareholders such that the aggregate number of H&F
Directors shall be not less than one. For so long as H&F has the power to have
at least one Director included in the slate of nominees recommended by the
Board, such power shall be exercised by HFCP IV (Bermuda), L.P.

      (f) Each of Warburg and H&F shall provide to the Company in a timely
manner all information required by Regulation 14A and Schedule 14A under the
Exchange Act with respect to each Warburg Director and each H&F Director,
respectively.

      Section 3.2. COMMITTEES OF THE BOARD. The Company and the Investors agree
that (1) for so long as there is at least one Warburg Director on the Board,
each committee of the Board shall include at least one Warburg Director, and (2)
for so long as there is at least one H&F Director on the Board, each committee
of the Board shall include at least one H&F Director. The foregoing is subject
to any restrictions on service on the audit committee as may be applicable under
the rules of Nasdaq or the SEC.

      Section 3.3. INVESTOR PROTECTION MATTERS. Except as specifically set forth
herein, in accordance with the Company's Bye-laws, the Board shall act by the
vote of a majority of the Directors present at a meeting, and the required
quorum for a meeting of the Board shall be a majority of the whole Board.
Notwithstanding the foregoing, and except as specifically set forth in the
Subscription Agreement, (a) prior to the Approval Date, unless also approved by
the Initial Warburg Director and the Initial H&F Director, and (b) following the
Approval Date, unless also approved by (i) at least one Warburg Director, if at
such time the Warburg Retained Percentage equals or exceeds 25%, and (ii) at
least one H&F Director, if at such time the H&F Retained Percentage equals or
exceeds 50%, the Company shall not (and shall not permit any of its Subsidiaries
to):

            (1) amend, or propose to amend, its certificate of incorporation,
      memorandum of association, bye-laws, or other organizational documents, or
      amend, terminate or waive any provision under, the Subscription Agreement
      or any other Agreement entered into in connection therewith;

            (2) split, consolidate, combine, subdivide, redeem or reclassify its
      share capital or other equity interests, or amend any term of the
      outstanding securities of the Company or its Subsidiaries;

            (3) declare, set aside, make or pay any dividend or other
      distribution in respect of its share capital or other equity interests, or
      purchase or redeem, directly or indirectly, any share capital or other
      equity interests (other than (A) dividends by a Sub-
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                                      -11-

      sidiary of the Company to the Company or a Subsidiary of the Company, and
      (B) dividends or other distributions by any entity in which the Company or
      any Subsidiary owns a minority interest, made in the normal course of
      business, consistent with past practice);

            (4) other than with respect to grant or exercise under the [existing
      Management Options] or the Long Term Incentive Plan for New Employees,
      issue, deliver or sell, or authorize the issuance, delivery or sale of,
      any share capital of any class, any equity interest, or any options,
      warrants, conversion or other rights to purchase any such shares or equity
      interests, or any securities convertible into or exchangeable for such
      shares or equity interests, or issue or authorize the issuance of any
      other security in respect of or in lieu of or in substitution for shares
      of capital or equity interests, or enter into any agreements restricting
      the transfer of, or affecting the rights of holders of, Common Shares,
      grant any preemptive or anti-dilutive rights to any holder of any class of
      securities of the Company, or grant registration rights with respect to
      any of the Company's securities;

            (5) amend or waive any rights under any grants made under the Long
      Term Incentive Plan for New Employees;

            (6) incur any indebtedness for borrowed money, guarantee any such
      indebtedness or issue or sell any debt securities, in excess of $5,000,000
      in the aggregate, or prepay or refinance any indebtedness for borrowed
      money;

            (7) engage in any Interested Party Transaction;

            (8) acquire any assets or properties for cash or otherwise for an
      amount in excess of $5,000,000 in the aggregate;

            (9) acquire, whether by means of merger, stock or asset purchase,
      joint venture or other similar transaction, any equity interest in, or all
      or substantially all of the assets of any Person, or any business or
      division of any Person;

            (10) replace the independent auditors of the Company or make any
      material change in any method of financial accounting or accounting
      practice, except for any such change required by reason of a concurrent
      change in U.S. generally accepted accounting principles;

            (11) sell or otherwise dispose of assets material to the Company and
      its Subsidiaries taken as a whole, except as specifically contemplated by
      the Subscription Agreement;
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                                      -12-

            (12) increase by 5% or more the annual base compensation of any
      officer or key employee of the Company, or enter into or make any material
      change in any severance contract or arrangement with any such officer or
      key employee;

            (13) consummate a complete liquidation or dissolution of the
      Company, a merger or consolidation (A) in which the Company or any
      Subsidiary is a constituent corporation or (B) with respect to which the
      Common Shares would have the right to vote under applicable law, a sale of
      all or substantially all of the Company's assets, or any similar business
      combination;

            (14) enter into any transaction involving in excess of $1,000,000,
      or, if such transaction is in the ordinary course of business consistent
      with past practice, $5,000,000;

            (15) approve the annual plan, annual capital expenditure budget or
      the five-year plan of the Company and its Subsidiaries, taken as a whole;

            (16) remove the Chief Executive Officer or Chairman of the Company,
      or appoint a new Chief Executive Officer or Chairman of the Company; or

            (17) enter into any agreement with respect to the foregoing.

Nothing in this Section 3.3 shall grant either H&F or Warburg any right or
consent (to the extent that such right would result in such party being deemed
to "control" an insurance subsidiary of the Company that is domiciled in any
state in the United States, where the exercise of such control would otherwise
require the prior approval of such state). In addition, the rights of Warburg
and H&F set forth in this Section 3.3 shall, in any event, terminate upon the
mandatory conversion of the Preference Shares under paragraph (g)(2) of the
Certificate of Designations for the Preference Shares (the "MANDATORY CONVERSION
DATE") or the earlier conversion of all Preference Shares in accordance with
their terms.

      Section 3.4. VOTING. Each Investor agrees to vote all Voting Securities
Beneficially Owned by such Investor or by any controlled Affiliate of such
Investor in favor of the proposals to be submitted for approval of the
shareholders of the Company at the special general meeting of the Company's
shareholders to be held in connection with the Transactions.

      Section 3.5. CHAIRMAN OF THE COMPANY. For so long as he is willing and
able to serve as the Chairman of the Company, Warburg and H&F agree to take such
actions as may be necessary to cause Robert Clements to be duly elected as
Chairman of the Company.

      Section 3.6. CERTAIN TRANSACTIONS. For a period of two years after the
Closing, except for transactions specifically contemplated by this Agreement,
the Related Agreements (as
<Page>

                                      -13-

defined in the Subscription Agreement) or the Purchased Securities, neither
Warburg nor H&F nor any of their respective Affiliates will, directly or
indirectly, without the prior approval of a majority of the Independent
Directors: (a) acquire securities or assets from the Company or any of its
Subsidiaries, (b) engage in any "Rule 13e-3 transaction" (as such term is
defined in Rule 13e-3(a)(3) under the Securities Exchange Act of 1934, as
amended) involving the Company, or (c) engage in any other transaction that
would result in the compulsory acquisition of Common Shares. The Company shall
not agree to amend this Section 3.6, without the prior approval of a majority of
the Independent Directors. The Company, Warburg and H&F shall endeavor to
include at all times two Independent Directors on the Board.

                                   ARTICLE IV

                               REGISTRATION RIGHTS

      Section 4.1. DEMAND REGISTRATIONS. (a) Warburg may at any time following
the date hereof and on not more than five separate occasions in the aggregate
and not more frequently than once during any 180 day period, require the Company
to file a registration statement under the Securities Act in respect of all or a
portion of the Common Shares, or the Common Shares into which Investor Shares
may be converted, then Beneficially Owned by Warburg or by any other person that
Beneficially Owns Common Shares and who acquired such Common Shares or Investor
Shares in connection with such person's status as a partner in any partnership
in which Warburg or any of its Affiliates is the general partner (all such
Common Shares, the "WARBURG REGISTRABLE SHARES") (provided that such request
covers Warburg Registrable Shares with a Market Value on the date of the Demand
Request of at least $25 million), by delivering to the Company a written notice
stating that such right is being exercised, specifying the number of Common
Shares to be included in such registration (the shares subject to such request,
the "WARBURG DEMAND SHARES") and describing the intended method of distribution
thereof (a "WARBURG DEMAND REQUEST"). Upon receiving a Warburg Demand Request,
the Company shall (1) provide written notice of the Warburg Demand Request,
pursuant to Section 4.3 hereof, to H&F and each other Investor, (2) use
reasonable efforts to file as promptly as reasonably practicable a registration
statement on such form as the Company may reasonably deem appropriate providing
for the registration of the sale of such Warburg Demand Shares and any other
Investor Shares to be included pursuant to Sections 4.3 and 4.4 hereof pursuant
to the intended method of distribution and (3) after the filing of an initial
version of the registration statement, use reasonable efforts to cause such
registration statement to be declared effective under the Securities Act as
promptly as practicable after the date of filing of such registration statement.
Any Demand Registration filed pursuant to the request of Warburg may, subject to
the provisions of Section 4.4 below, include other Common Shares that the
Company is required to include in such registration statement by virtue of
<Page>

                                      -14-

existing agreements between the holders of such Common Shares and the Company
(the "EXISTING REGISTRATION RIGHTS").

      (b) H&F may at any time following the date hereof and on not more than
five separate occasions in the aggregate and not more frequently than once
during any 180 day period, require the Company to file a registration statement
under the Securities Act in respect of all or a portion of the Common Shares, or
the Common Shares into which Investor Shares may be converted, then Beneficially
Owned by H&F or by any other person that Beneficially Owns Common Shares and who
acquired such Common Shares or Investor Shares in connection with such person's
status as a partner in any partnership in which H&F or any of its Affiliates is
the general partner (all such Common Shares, the "H&F REGISTRABLE SHARES," and
together with the Warburg Registrable Shares, the "REGISTRABLE SHARES")
(provided that such request covers H&F Registrable Shares with a Market Value on
the date of the Demand Request of at least $25 million), by delivering to the
Company a written notice stating that such right is being exercised, specifying
the number of Common Shares to be included in such registration (the shares
subject to such request, the "H&F DEMAND SHARES") and describing the intended
method of distribution thereof (a "H&F DEMAND REQUEST"). Upon receiving a H&F
Demand Request, the Company shall (1) provide written notice of the H&F Demand
Request, pursuant to Section 4.3 hereof, to Warburg and each other Investor, (2)
use reasonable efforts to file as promptly as reasonably practicable a
registration statement on such form as the Company may reasonably deem
appropriate providing for the registration of the sale of such H&F Demand Shares
and any other Investor Shares to be included therein pursuant to Section 4.3 and
4.4 hereof pursuant to the intended method of distribution, and (3) after the
filing of an initial version of the registration statement, use reasonable
efforts to cause such registration statement to be declared effective under the
Securities Act as promptly as practicable after the date of filing of such
registration statement. Any Demand Registration filed pursuant to the request of
H&F may, subject to the provisions of Section 4.4 below, include other Common
Shares that the Company is required to include in such registration statement by
virtue of the Existing Registration Rights.

      (c) Notwithstanding anything in this Agreement to the contrary, the
Company shall be entitled to postpone and delay, for reasonable periods of time
not to exceed 60 consecutive days and in no event to exceed more than an
aggregate of 90 days during any 360-day period (a "BLACKOUT PERIOD"), the filing
or effectiveness of any Demand Registration if the Board shall determine that
any such filing or the offering of any Registrable Shares would (1) in the good
faith judgment of the Board, impede, delay or otherwise interfere with any
pending or contemplated acquisition, corporate reorganization or other similar
material transaction involving the Company (each, a "MATERIAL TRANSACTION"), (2)
based upon advice from the Company's investment banker or financial advisor,
adversely affect any pending or contemplated financing, offering or sale of any
class of securities by the Company, or (3) in the good faith judgment of the
Board, require disclosure of material non-public information (other than
in-
<Page>

                                      -15-

formation relating to an event described in clauses (1) or (2) above) which, if
disclosed at such time, would be harmful to the best interests of the Company
and its shareholders. Upon notice by the Company to each Investor of any such
determination, such Investor shall keep the fact of any such notice strictly
confidential, and during any Blackout Period promptly halt any offer, sale,
trading or transfer by it or any of its Subsidiaries of any Common Shares for
the duration of the Blackout Period set forth in such notice (or until such
Blackout Period shall be earlier terminated in writing by the Company) and
promptly halt any use, publication, dissemination or distribution of the Demand
Registration, each prospectus included therein, and any amendment or supplement
thereto by it for the duration of the Blackout Period set forth in such notice
(or until such Blackout Period shall be earlier terminated in writing by the
Company) and, if so directed by the Company, will deliver to the Company any
copies then in its possession of the prospectus covering such Registrable
Shares.

      (d) In case a Demand Registration has been filed, if a Material
Transaction has occurred, the Company may cause such Demand Registration to be
withdrawn and its effectiveness terminated or may postpone amending or
supplementing such Demand Registration for a reasonable period of time;
provided, however, that in no event shall a Demand Registration so withdrawn by
the Company count for the purposes of determining the number of Demand
Registrations to which either Warburg or H&F is entitled under Section 4.1(a) or
(b).

      (e) In connection with any underwritten offering under this Section 4.1,
the managing underwriter for such Demand Registration shall be jointly selected
by Warburg and H&F, provided that such managing underwriter shall be a
nationally recognized investment banking firm.

      (f) Nothing in this Article IV shall affect or supersede any of the
transfer restrictions set forth in Article V hereof or any of the other
provisions of this Agreement.

      Section 4.2. SHELF REGISTRATION. At the request of either Warburg or H&F,
the Company shall use reasonable best efforts to file a registration statement
on Form S-3, or any successor form thereto, covering the offering of Common
Shares by Investors (subject to the provisions of Section 5.2 hereof) on a
delayed or continuous basis (the "SHELF REGISTRATION STATEMENT") to be effective
as soon as reasonably practicable following the Closing Date. Upon effectiveness
of the Shelf Registration Statement, the Company will use its reasonable best
efforts to keep the Shelf Registration Statement effective with the SEC until
such time the Common Shares held by all Investors are freely tradable under Rule
144(k) under the Securities Act. Notwithstanding the foregoing, the Company may
suspend the effectiveness of the Shelf Registration Statement during any
Blackout Period.

      Section 4.3. PIGGY-BACK REGISTRATION. If, at any time following the date
hereof, the Company proposes to register any Common Shares under the Securities
Act on its behalf or on behalf of any of its shareholders (including pursuant to
a Demand Registration), on a form
<Page>

                                      -16-

and in a manner that would permit registration of Common Shares (other than in
connection with dividend reinvestment plans, rights offerings or a registration
statement on Form S-4 or S-8 or any similar successor form), the Company shall
give reasonably prompt written notice to each Investor of its intention to do
so. Upon the written election of any Investor (a "PIGGY-BACK REQUEST"), given
within ten Business Days following the receipt by such Investor of any such
written notice (which election shall specify the number of the Registrable
Shares intended to be disposed of by such Investor), the Company shall include
in such registration statement (a "PIGGY-BACK REGISTRATION"), subject to the
provisions of Section 4.4 hereof, such number of the Registrable Shares as shall
be set forth in such Piggy-Back Request.

      Section 4.4. ALLOCATION OF SHARES TO BE REGISTERED. In the event that the
Company proposes to register Common Shares in connection with an underwritten
offering and a nationally recognized investment banking firm selected by the
Company, or in the case of a Demand Registration by the Investors, to act as
managing underwriter thereof reasonably and in good faith shall have advised the
Company and each Investor in writing that, in its opinion, the inclusion in the
registration statement of some or all of the Registrable Shares sought to be
registered in a Piggy-Back Request would adversely affect the price or success
of the offering, the Company shall include in such registration statement such
number of Common Shares as the Company is advised can be sold in such offering
without such an effect (the "MAXIMUM NUMBER") as follows and in the following
order of priority: (a) FIRST, if such registration is not in connection with a
Demand Registration, such number of Common Shares, if any, as the Company
intended to be registered by the Company for its own account, or to be
registered pursuant to Existing Registration Rights, to the extent such Existing
Registration Rights so require; (b) SECOND, if and to the extent that the number
of Common Shares to be registered under clause (a) is less than the Maximum
Number (or because the registration is a Demand Registration in which the
Company is not permitted to offer Common Shares), such number of Registrable
Shares as Warburg and H&F (and, to the extent required by any Existing
Registration Rights, any other holder of Common Shares having such rights) shall
have intended to register which, when added to the number of Common Shares to be
registered under clause (a), is less than or equal to the Maximum Number, it
being understood that the number of shares included by Warburg and H&F (and such
other holders under Existing Registration Rights) shall be cut back, if
necessary, in proportion to their relative ownership at the time; and (c) third,
if and to the extent that the number of Common Shares to be registered under
clause (b) is less than the Maximum Number, such number of Registrable Shares as
the Participating Investors (other than Warburg and H&F (and such other holders
under Existing Registration Rights)) shall have intended to register which, when
added to the number of Common Shares to be registered under clauses (a) and (b),
is less than or equal to the Maximum Number, it being understood that the number
of shares included by the Investors (other than Warburg and H&F and such other
holders under Existing Registration Rights)) shall be cut back, if necessary, in
proportion to their relative ownership.
<Page>

                                      -17-

      Section 4.5. REGISTRATION PROCEDURES. (a) In connection with each
registration statement prepared pursuant to this Article IV, and in accordance
with the intended method or methods of distribution of the Common Shares as
described in such registration statement, the Company shall, as soon as
reasonably practicable and to the extent practicable:

            (1) prepare and file with the SEC a registration statement on an
      appropriate registration form and use reasonable efforts to cause such
      registration statement to become and remain effective as promptly as
      reasonably practicable; PROVIDED that before filing a registration
      statement or prospectus or any amendments or supplements thereto, the
      Company shall furnish to counsel to H&F and Warburg, if disposing of
      Registrable Shares under such registration statement, draft copies of all
      such documents proposed to be filed at least five days prior to such
      filing, which documents will be subject to the reasonable review of each
      of H&F and Warburg, as appropriate, and its agents and representatives;

            (2) furnish without charge to each Participating Investor, and the
      managing underwriter or underwriters, if any, at least one conformed copy
      of the registration statement and each post-effective amendment or
      supplement thereto (but excluding schedules, all documents incorporated or
      deemed incorporated therein by reference and all exhibits, unless
      requested in writing by such Participating Investor or such underwriter)
      and such number of copies of the summary, preliminary, final, amended or
      supplemented prospectuses included in such registration statement as such
      Participating Investor or such underwriter may reasonably request;

            (3) except with respect to a Shelf Registration Statement, the
      obligations of the Company with respect to the effectiveness thereof to be
      governed by Section 4.2, use reasonable best efforts to keep such
      registration statement effective for the earlier of (A) 180 days and (B)
      such time as all of the securities covered by the registration statement
      have been disposed (the "EFFECTIVE PERIOD"); prepare and file with the SEC
      such amendments, post-effective amendments and supplements to the
      registration statement and the prospectus as may be necessary to maintain
      the effectiveness of the registration for the Effective Period and to
      cause the prospectus (and any amendments or supplements thereto) to be
      filed;

            (4) use reasonable efforts to register or qualify the Registrable
      Shares covered by such registration statement under such other securities
      or "blue sky" laws of such jurisdictions in the United States as are
      reasonably necessary, keep such registrations or qualifications in effect
      for so long as the registration statement remains in effect, and do any
      and all other acts and things which may be reasonably necessary to enable
      each Participating Investor or any underwriter to consummate the
      disposition of the Common Shares in such jurisdictions;
<Page>

                                      -18-

            (5) use reasonable efforts to cause the Registrable Shares to be
      registered with or approved by such other governmental agencies or
      authorities as may be necessary to enable each Participating Investor to
      consummate the disposition of the Registrable Shares;

            (6) use reasonable efforts to cause all Registrable Shares covered
      by such registration statement to be listed on the Nasdaq or on the
      principal securities exchange on which the Common Shares are then listed;

            (7) promptly notify each Participating Investor and the managing
      underwriter or underwriters, if any, after becoming aware thereof, (A)
      when the registration statement or any related prospectus or any amendment
      or supplement thereto has been filed, and, with respect to the
      registration statement or any post-effective amendment, when the same has
      become effective, (B) of any request by the SEC for amendments or
      supplements to the registration statement or the related prospectus or for
      additional information, (C) of the issuance by the SEC of any stop order
      suspending the effectiveness of the registration statement or the
      initiation of any proceedings for that purpose, (D) of the receipt by the
      Company of any notification with respect to the suspension of the
      qualification of the Registrable Shares for sale in any jurisdiction or
      the initiation of any proceeding for such purpose or (E) within the
      Effective Period of the happening of any event or the existence of any
      fact that makes any statement in the registration statement or any
      post-effective amendment thereto, prospectus or any amendment or
      supplement thereto, or any document incorporated therein by reference
      untrue in any material respect or which requires the making of any changes
      in the registration statement or post-effective amendment thereto or any
      prospectus or amendment or supplement thereto so that they will not
      contain any untrue statement of a material fact or omit to state any
      material fact required to be stated therein or necessary to make the
      statements therein, in light of the circumstances under which they were
      made, not misleading;

            (8) during the Effective Period, use its reasonable efforts to
      obtain the withdrawal of any order enjoining or suspending the use or
      effectiveness of the registration statement or any post-effective
      amendment thereto;

            (9) deliver promptly to each of Warburg and H&F, if disposing of
      Common Shares under such registration statement, copies of all
      correspondence between the SEC and the Company, its counsel or auditors
      and all memoranda relating to discussions with the SEC or its staff with
      respect to the registration statement and permit each of Warburg and H&F,
      if disposing of Common Shares under such registration statement, to do
      such investigation, with respect to information contained in or omitted
      from the registration statement, as it reasonably deems necessary;
<Page>

                                      -19-

            (10) in the case of an underwritten offering, use best efforts to
      enter into an underwriting agreement customary in form and scope for
      underwritten secondary offerings of the nature contemplated by the
      applicable registration statement;

            (11) provide a transfer agent and registrar for all such Registrable
      Shares covered by such registration statement not later than the effective
      date of such registration statement, subject to any applicable laws or
      regulations; and

            (12) cooperate with each Participating Investor and the managing
      underwriter or underwriters, if any, to facilitate the timely preparation
      and delivery of certificates representing such Registrable Shares to be
      sold under the registration statement; and, in the case of an underwritten
      offering, enable such Registrable Shares to be in such denominations and
      registered in such names as the managing underwriter or underwriters, if
      any, may request in writing at least two Business Days prior to any sale
      of the Registrable Shares to the underwriters.

      (b) In the event that the Company would be required, pursuant to Section
4.5(a)(7)(E) above, to notify each Participating Investor or the managing
underwriter or underwriters, if any, of the happening of any event specified
therein, the Company shall, subject to the provisions of Section 4.1(c) hereof,
as promptly as practicable, prepare and furnish to each Participating Investor
and to each such underwriter a reasonable number of copies of a prospectus
supplemented or amended so that, as thereafter delivered to purchasers of
Registrable Shares that have been registered pursuant to this Agreement, such
prospectus shall not contain an untrue statement of a material fact or omit to
state a material fact required to be stated therein or necessary to make the
statements therein, in the light of the circumstances under which they were
made, not misleading. Each Participating Investor agrees that, upon receipt of
any notice from the Company pursuant to Section 4.5(a)(7)(E) hereof, it shall,
and shall use its reasonable best efforts to cause any sales or placement agent
or agents for the Registrable Shares and the underwriters, if any, to, forthwith
discontinue disposition of the Registrable Shares until such Person shall have
received copies of such amended or supplemented prospectus and, if so directed
by the Company, to destroy or to deliver to the Company all copies, other than
permanent file copies, then in its possession of the prospectus (prior to such
amendment or supplement) covering such Registrable Shares as soon as practicable
after such Participating Investor's receipt of such notice.

      (c) Each Participating Investor shall furnish to the Company in writing
its intended method of distribution of the Registrable Shares it proposes to
dispose of and such other information as the Company may from time to time
reasonably request in writing, but only to the extent that such information is
required in order for the Company to comply with its obligations under all
applicable securities and other laws and to ensure that the prospectus relating
to such Registrable Shares conforms to the applicable requirements of the
Securities Act.
<Page>

                                      -20-

Each Participating Investor shall notify the Company as promptly as practicable
of any inaccuracy or change in information previously furnished by such
Participating Investor to the Company or of the occurrence of any event, in
either case as a result of which any prospectus relating to the Registrable
Shares contains or would contain an untrue statement of a material fact or omits
to state any material fact required to be stated therein or necessary to make
the statements therein, in light of the circumstances under which they were
made, not misleading, and promptly furnish to the Company any additional
information required to correct and update any previously furnished information
or required so that such prospectus shall not contain an untrue statement of a
material fact or omit to state a material fact required to be stated therein or
necessary to make the statements therein, in light of the circumstances under
which they were made, not misleading.

      (d) In the case of any registration under Section 4.1 hereof pursuant to
an underwritten offering, or in the case of a registration under Section 4.3
hereof if the Company has determined to enter into an underwriting agreement in
connection therewith, all Common Shares to be included in such registration
shall be subject to the applicable underwriting agreement and no Person may
participate in such registration unless such Person agrees to sell such Person's
securities on the basis provided therein and completes and executes all
questionnaires, indemnities, underwriting agreements and other documents (other
than powers of attorney) which must be executed in connection therewith, and
provides such other information to the Company or the underwriter as may be
reasonably requested to register such Person's Common Shares.

      Section 4.6. REGISTRATION EXPENSES. The Company shall bear all
registration and filing fees, fees and expenses of compliance with securities or
blue sky laws, fees and expenses in connection with the review of underwriting
arrangements by the NASD Regulation, Inc. (including the fees of any "qualified
independent underwriter"), agent fees and commissions, printing costs and fees
and disbursements of its counsel, and of one counsel as may be reasonably
selected by the Participating Investors, and accountants, in each case, in
connection with any registration and listing of any Common Shares pursuant to
Section 4.1, 4.2 or 4.3, other than underwriting discounts or commissions in
connection with the Registrable Shares disposed of by any Participating
Investor, which shall be borne by such Participating Investor.

      Section 4.7. INDEMNIFICATION; CONTRIBUTION. (a) The Company shall, and it
hereby agrees to, indemnify and hold harmless each Participating Investor and
its officers, directors, employees and controlling Persons, if any, and each
underwriter, its partners, officers, directors, employees and controlling
Persons, if any, in any offering or sale of Common Shares, against any losses,
claims, damages or liabilities to which each such indemnified party may become
subject, insofar as such losses, claims, damages or liabilities, or actions or
proceedings in respect thereof, including any amounts paid in settlement as
provided herein (collectively, "CLAIMS"), arise out of or are based upon an
untrue state-
<Page>

                                      -21-

ment or alleged untrue statement of a material fact contained in any
registration statement, or any preliminary or final prospectus contained
therein, or any amendment or supplement thereto, or any document incorporated by
reference therein, or arise out of or are based upon any omission or alleged
omission to state therein a material fact required to be stated therein or
necessary to make the statements therein, in light of the circumstances in which
they were made, not misleading, and the Company shall, and it hereby agrees to,
reimburse each Participating Investor or any such underwriter for any legal or
other out-of-pocket expenses reasonably incurred by it in connection with
investigating or defending any such Claims; PROVIDED, HOWEVER, that the Company
shall not be liable to any such Person in any such case to the extent that any
such Claims arise out of or are based upon an untrue statement or alleged untrue
statement or omission or alleged omission made in such registration statement,
or preliminary or final prospectus, or amendment or supplement thereto, in
reliance upon and in conformity with information furnished in writing to the
Company by such Participating Investor or any underwriter expressly for use
therein.

      (b) Each Participating Investor shall, and hereby agrees to (1) indemnify
and hold harmless the Company, its directors, officers, employees and
controlling Persons, if any, and each underwriter, its partners, officers,
directors, employees and controlling Persons, if any, in any offering or sale of
Common Shares, against any Claims to which each such indemnified party may
become subject, insofar as such Claims arise out of or are based upon an untrue
statement or alleged untrue statement of a material fact contained in such
registration statement, or any preliminary or final prospectus contained
therein, or any amendment or supplement thereto, or any document incorporated by
reference therein, or arise out of or are based upon any omission or alleged
omission to state therein a material fact required to be stated therein or
necessary to make the statements therein not misleading, in each case only to
the extent that such untrue statement or alleged untrue statement or omission or
alleged omission was made in reliance upon and in conformity with written
information furnished to the Company by such Participating Investor expressly
for use therein, and (2) reimburse the Company for any legal or other
out-of-pocket expenses reasonably incurred by the Company in connection with
investigating or defending any such Claim.

      (c) Promptly after receipt by an indemnified party under Section 4.7(a) or
Section 4.7(b) of written notice of the commencement of any action or proceeding
for which indemnification under Section 4.7(a) or Section 4.7(b) may be
requested, such indemnified party shall notify the indemnifying party in writing
of the commencement of such action or proceeding, but the omission so to notify
the indemnifying party shall not relieve it from any liability which it may have
to any indemnified party in respect of such action or proceeding hereunder
unless the indemnifying party was materially prejudiced by such failure of the
indemnified party to give such notice, and in no event shall such omission
relieve the indemnifying party from any other liability it may have to such
indemnified party. In case any such action or proceeding shall be brought
against any indemnified party and it shall notify an indemnifying
<Page>

                                      -22-

party of the commencement thereof, such indemnifying party shall be entitled to
participate therein and, to the extent that it shall determine, jointly with any
other indemnifying party similarly notified, to assume the defense thereof, with
counsel reasonably satisfactory to such indemnified party, and, after notice
from the indemnifying party to such indemnified party of its election so to
assume the defense thereof, such indemnifying party shall not be liable to such
indemnified party for any legal or any other expenses subsequently incurred by
such indemnified party in connection with the defense thereof other than
reasonable costs of investigation. If the indemnifying party is not entitled to,
or elects not to, assume the defense of a claim, it will not be obligated to pay
the fees and expenses of more than one counsel for each indemnified party with
respect to such claim. The indemnifying party will not be subject to any
liability for any settlement made without its consent, which consent shall not
be unreasonably withheld or delayed. No indemnifying party shall, without the
prior written consent of the indemnified party, compromise or consent to entry
of any judgment or enter into any settlement agreement with respect to any
action or proceeding in respect of which indemnification is sought under Section
4.7(a) or Section 4.7(b) (whether or not the indemnified party is an actual or
potential party thereto), unless such compromise, consent or settlement includes
an unconditional release of the indemnified party from all liability in respect
of such claim or litigation and does not subject the indemnified party to any
material injunctive relief or other material equitable remedy.

      (d) Each Participating Investor and the Company agree that if, for any
reason, the indemnification provisions contemplated by Sections 4.7(a) or 4.7(b)
hereof are unavailable to or are insufficient to hold harmless an indemnified
party in respect of any Claims referred to therein (other than as a result of
the provisos thereto), then each indemnifying party shall contribute to the
amount paid or payable by such indemnified party as a result of such Claims in
such proportion as is appropriate to reflect the relative fault of and benefits
derived by the indemnifying party, on the one hand, and the indemnified party,
on the other hand, as well as other equitable considerations. The amount paid or
payable by an indemnified party as a result of the Claims referred to above
shall be deemed to include (subject to the limitations set forth in Section
4.7(c) hereof) any legal or other fees or expenses reasonably incurred by such
indemnified party in connection with investigating or defending any such action,
proceeding or claim. No Person guilty of fraudulent misrepresentation (within
the meaning of Section 11(f) of the Securities Act) shall be entitled to
contribution from any Person who was not guilty of such fraudulent
misrepresentation.
<Page>

                                      -23-

                                    ARTICLE V

            TAG-ALONG RIGHTS; RESTRICTIONS ON TRANSFER AND CONVERSION

      Section 5.1. TAG-ALONG RIGHTS. In the event that Warburg or H&F proposes
to sell, convey, dispose or otherwise transfer Initial Shares (such party
proposing to sell, the "SELLING INVESTOR") in a bona fide transaction to an
un-Affiliated third party, or in a series of related bona fide transactions to
multiple un-Affiliated third parties, and the net proceeds of such sale are
reasonably expected to exceed $50 million (such a transaction, or series of
related transactions, a "THIRD PARTY SALE"), such Selling Investor shall notify
the other Investor (such other Investor, the "TAG-ALONG INVESTOR") in writing of
such Third Party Sale, which notice shall set forth the material terms of such
Third Party Sale, including, without limitation, the number of Initial Shares
proposed to be sold and the per share price thereof (the "THIRD PARTY SALE
NOTICE"). Such Tag-Along Investor shall have the right, but not the obligation,
to participate in such Third Party Sale upon providing the Selling Investor
written notice of intent to exercise such right within ten Business Days of the
receipt of Third Party Sale Notice. Such notice shall set forth the number of
Initial Shares that such Tag-Along Investor desires to sell in such Third Party
Sale, which such number shall not exceed that number of Initial Shares equal to
the product of (a) the number of Initial Shares set forth in the Third Party
Sale Notice, and (b) the quotient of (1) the Retained Percentage of the
Tag-Along Investor, over (2) the sum of (A) the Retained Percentage of the
Selling Investor, and (B) the Retained Percentage of the Tag-Along Investor.
Notwithstanding the foregoing, this Section 5.1 shall not be applicable to any
sale effected in the public markets (including by means of a "block trade"
effected through any registered broker-dealer), or to any distribution to
partners of any partnership in which either Warburg or H&F, or any of their
respective Affiliates, is the general partner.

      Section 5.2. RESTRICTIONS ON TRANSFER. Until the earliest to occur of (a)
the first anniversary of the Closing, (b) the occurrence of any event that would
cause Company's outstanding Class B Warrants to vest and/or become exercisable,
or (c) the completion by the Company of a registered public offering of Common
Shares the net proceeds to the Company of which exceed $25 million, (1) Warburg
agrees that it will not sell, dispose, convey or otherwise transfer any Initial
Warburg Shares if, following the consummation of such sale, the Retained Warburg
Percentage would be less that 66%, and (2) H&F agrees that it will not sell,
dispose, convey or otherwise transfer any Initial H&F Shares if, following the
consummation of such sale, the Retained H&F Percentage would be less that 66%.
Following the earliest to occur of clauses (a), (b) or (c) in the preceding
sentence, there shall be no restrictions on transfer of any Initial Warburg
Shares or any Initial H&F Shares, except as may be imposed by applicable law,
including by the Securities Act. Nothing in this Section 5.2 shall be deemed to
affect any disposition of Initial Shares pursuant to the terms of any merger,
consolidation or other business combination transaction, or to the tender of any
Initial Shares into any tender or
<Page>

                                      -24-

exchange offer, PROVIDED, that such merger, consolidation or other business
combination has been approved by, or such tender or exchange offer has been
recommended to, the shareholders of the Company by, the Board.

      Section 5.3. RESTRICTIONS ON CONVERSION. Prior to receipt of the Requisite
Shareholder Approval, no Investor shall convert any Preference Shares into
Common Shares if such conversion would result in the delisting of the Common
Shares by Nasdaq. Prior to receipt of the Requisite Regulatory Approval, no
Investor shall convert any Preference Shares into Common Shares unless all
necessary approvals for such ownership of Common Shares have been obtained, it
being understood that, subject to Section 5.2 hereof, this restriction on
conversion shall not restrict an Investor from converting and selling, or
otherwise disposing of, the shares received on conversion in such a manner as
would not result in violation of any applicable regulation.

                                   ARTICLE VI

                 RESTRICTIONS ON DIVIDENDS AND SHARE REPURCHASES

      The Company shall not declare any dividend or make any other distribution
on, or in respect of, any Common Shares, and shall not repurchase any Common
Shares, until such time as the Company has repurchased from Warburg and H&F, in
proportion to their respective Retained Percentages at the time of such
repurchase, Initial Shares having an aggregate value of $250 million, at a per
share price acceptable to Warburg and H&F.

                                   ARTICLE VII

                          EFFECTIVENESS AND TERMINATION

      Section 7.1. EFFECTIVENESS. This Agreement shall take effect immediately
upon the Closing and shall remain in effect until it is terminated pursuant to
Section 7.2 hereof.

      Section 7.2. TERMINATION. Other than with respect to Article IV hereof and
with respect to the termination provisions specifically elsewhere set forth in
this Agreement as may be applicable to any particular Section of this Agreement,
this Agreement shall terminate upon the latest to occur of the following:

            (a) the tenth anniversary of the Closing; or
<Page>

                                      -25-

            (b) mutual written agreement of the Company, Warburg and H&F at any
      time to terminate this Agreement.

                                  ARTICLE VIII

                                  MISCELLANEOUS

      Section 8.1. INJUNCTIVE RELIEF. Each party hereto acknowledges that it
would be impossible to determine the amount of damages that would result from
any breach of any of the provisions of this Agreement and that the remedy at law
for any breach, or threatened breach, of any of such provisions would likely be
inadequate and, accordingly, agrees that each other party shall, in addition to
any other rights or remedies which it may have, be entitled to seek such
equitable and injunctive relief as may be available from any court of competent
jurisdiction to compel specific performance of, or restrain any party from
violating, any of such provisions. In connection with any action or proceeding
for injunctive relief, each party hereto hereby waives the claim or defense that
a remedy at law alone is adequate and agrees, to the maximum extent permitted by
law, to have each provision of this Agreement specifically enforced against it,
without the necessity of posting bond or other security against it, and consents
to the entry of injunctive relief against it enjoining or restraining any breach
or threatened breach of such provisions of this Agreement.

      Section 8.2. SUCCESSORS AND ASSIGNS. This Agreement shall be binding upon,
and shall inure to the benefit of and be enforceable by the Company, Warburg and
H&F and their respective successors and permitted assigns, and no such term or
provision is for the benefit of, or intended to create any obligations to, any
other Person, except as otherwise specifically provided in this Agreement.
Neither this Agreement nor any rights or obligations hereunder shall be
assignable without the consent of each other party; provided, HOWEVER, that in
connection with any sale or transfer by Warburg or H&F of any Investor Shares,
the transferee of such Investor Shares may become a party hereto solely for
purposes of Article IV and Sections 3.4 and 5.3 hereof and have the rights of,
and be subject to the obligations of, an "Investor" upon due execution and
delivery of a counterpart signature page hereto.

      Section 8.3. AMENDMENTS; WAIVER. This Agreement may be amended only by an
agreement in writing executed by the parties hereto. Any party may waive in
whole or in part any benefit or right provided to it under this Agreement, such
waiver being effective only if contained in a writing executed by the waiving
party. No failure by any party to insist upon the strict performance of any
covenant, duty, agreement or condition of this Agreement or to exercise any
right or remedy consequent upon breach thereof shall constitute a waiver of any
such breach or of any other covenant, duty, agreement or condition, nor shall
any delay or
<Page>

                                      -26-

omission of any party to exercise any right hereunder in any manner impair the
exercise of any such right accruing to it thereafter.

      Section 8.4. NOTICES. Except as otherwise provided in this Agreement, all
notices, requests, claims, demands, waivers and other communications hereunder
shall be in writing and shall be deemed to have been duly given when delivered
by hand, when delivered personally or by facsimile transmission if promptly
electronically confirmed, as follows:

         If to the Company:

                  Arch Capital Group, Ltd.
                  20 Horseneck Lane
                  Greenwich, Connecticut 06830
                  Attention: General Counsel
                  Telephone: (203) 862-4300
                  Fax: (203) 861-7240

         with a copy to:

                  Cahill Gordon & Reindel
                  80 Pine Street
                  New York, New York 10005
                  Attention: Immanuel Kohn, Esq.
                  Telephone: (212) 701-3000
                  Fax: (212) 269-5420

         If to Warburg:

                  Warburg, Pincus Equity Partners, L.P.
                  466 Lexington Avenue
                  New York, New York 10017
                  Attention: Kewsong Lee
                  Telephone: (212) 878-0600
                  Fax: (212) 878-9100
<Page>

                                      -27-

         with a copy to:

                  Wachtell, Lipton, Rosen & Katz
                  51 West 52nd Street
                  New York, NY 10019
                  Attention: Andrew R. Brownstein, Esq.
                  Telephone: (212) 403-1000
                  Fax: (212) 403-2000

         If to H&F:

                  Hellman & Friedman LLC
                  One Maritime Plaza
                  Suite 1200
                  San Francisco, CA 94111
                  Attention: Richard M. Levine, Esq.
                  Telephone: (415) 788-5111
                  Fax: (415) 788-0176

         with a copy to:

                  Wachtell, Lipton, Rosen & Katz
                  51 West 52nd Street
                  New York, NY 10019
                  Attention: Patricia A. Vlahakis, Esq.
                  Telephone: (212) 403-1000
                  Fax: (212) 403-2000

or to such other address, facsimile number or telephone as either party may,
from time to time, designate in a written notice given in a like manner.

      Section 8.5. APPLICABLE LAW. Except to the extent of the applicability of
the Companies Law of Bermuda to this Agreement, this Agreement shall be governed
by and construed in accordance with the laws of the State of New York with
regard to contracts formed and to be entirely performed within such state
without giving effect to principles of conflicts of law.

      Section 8.6. HEADINGS. The descriptive headings of the several sections in
this Agreement are for convenience only and do not constitute a part of this
Agreement and shall not be deemed to limit or affect in any way the meaning or
interpretation of this Agreement. References to "Sections" and "Articles" herein
shall be to the Sections or Articles of this Agreement, unless the context
requires otherwise.
<Page>

                                      -28-

      Section 8.7. INTEGRATION. This Agreement and the other writings referred
to herein or delivered pursuant hereto which form a part hereof contain the
entire understanding of the parties with respect to its subject matter. This
Agreement supersedes all prior agreements and understandings between the parties
with respect to its subject matter.

      Section 8.8. SEVERABILITY. If any term or provision of this Agreement or
any application thereof shall be declared or held invalid, illegal or
unenforceable, in whole or in part, whether generally or in any particular
jurisdiction, such provision shall be deemed amended to the extent, but only to
the extent, necessary to cure such invalidity, illegality or unenforceability,
and the validity, legality and enforceability of the remaining provisions, both
generally and in every other jurisdiction, shall not in any way be affected or
impaired thereby.

      Section 8.9. CONSENT TO JURISDICTION. In connection with any suit, claim,
action or proceeding arising out of this Agreement, the parties each hereby
consent to the in personam jurisdiction of the United States federal courts and
state courts located in the Borough of Manhattan, City of New York, State of New
York; the Company, Warburg and H&F each agree that service in the manner set
forth in Section 8.4 hereof shall be valid and sufficient for all purposes; and
the parties each agree to, and irrevocably waive any objection based on forum
non conveniens or venue, appear in any United States federal court or state
court located in the Borough of Manhattan, City of New York, State of New York.

      Section 8.10. COUNTERPARTS. This Agreement may be executed by the parties
hereto in two or more counterparts, each of which shall be deemed an original,
but all of which together shall constitute one and the same instrument.
<Page>

                                      -29-

      IN WITNESS WHEREOF, the parties have caused this Agreement to be duly
executed by their respective authorized officers as of the date set forth at the
head of this Agreement.

                                                     ARCH CAPITAL GROUP, LTD.

                                                     By:
                                                         -----------------------
                                                         Name:
                                                         Title:

                                                     [_________]

                                                     By:
                                                         -----------------------
                                                         Name:
                                                         Title:

                                                     [_________]

                                                     By:
                                                         -----------------------
                                                         Name:
                                                         Title:

                                                     [_________]

                                                     By:
                                                         -----------------------
                                                         Name:
                                                         Title:

                                                     [_________]

                                                     By:
                                                         -----------------------
                                                         Name:
                                                         Title:

                                                     [_________]
<Page>

                                      -30-

                                                     By:
                                                         -----------------------
                                                         Name:
                                                         Title:

                                                     [_________]

                                                     By:
                                                         -----------------------
                                                         Name:
                                                         Title:

                                                     [_________]

                                                     By:
                                                         -----------------------
                                                         Name:
                                                         Title:

                                                     [_________]

                                                     By:
                                                         -----------------------
                                                         Name:
                                                         Title:

                                                     [_________]<Page>

                                                                    Exhibit 10.2

                             ARCH CAPITAL GROUP LTD.
                                20 Horseneck Lane
                               Greenwich, CT 06830

                                                                November 8, 2001

<Table>
<S>                                            <C>
The Trident Partnership, L.P. ("TRIDENT I")    Warburg Pincus Private Equity VIII, L.P.
Craig Appin House                              Warburg Pincus International Partners, L.P.
8 Wesley Street                                Warburg Pincus Netherlands International
Hamilton HM 11 Bermuda                              Partners I, C.V.
                                               Warburg Pincus Netherlands International
Trident II, L.P. ("TRIDENT II")                     Partners II, C.V.
Craig Appin House                              (collectively, "WARBURG")
8 Wesley Street                                466 Lexington Avenue
Hamilton HM 11 Bermuda                         New York, NY  10017

Marsh & McLennan Capital Professionals         HFCP IV (Bermuda), L.P. ("H&F")
     Fund, L.P.                                c/o Hellman & Friedman LLC
Marsh & McLennan Employees' Securities         One Maritime Plaza
     Company, L.P.                             Suite 1200
(together, the "CO-INVESTMENT FUNDS")          San Francisco, CA  94111
c/o Maples and Calder Ugland House
South Church Street
George Town Grand Cayman
Cayman Islands, British West Indies

Marsh & McLennan Risk Capital Holdings,
     Ltd. ("MARSH")
1166 Avenue of the Americas
New York, NY  10036
</Table>

Ladies and Gentlemen:

                  This letter agreement (this "AGREEMENT") confirms the
agreement reached today among each of the parties signatories hereto regarding
the participation of Trident II and the Co-Investment Funds in the purchase of a
portion of the Securities, as contemplated by, and on the terms set forth in,
this Agreement and the Subscription Agreement dated as of October 24, 2001 (the
"SUBSCRIPTION AGREEMENT") by and among Arch Capital Group Ltd.

<Page>
                                      -2-

("ARCH"), Warburg and H&F (the "PURCHASERS"), and certain other matters in
connection therewith. Capitalized terms used herein without definition shall
have the meanings ascribed to such terms in the Subscription Agreement.

                  1. INVESTMENT BY TRIDENT II. Warburg hereby assigns, without
recourse or warranty by it, to Trident II and the Co-Investment Funds
(collectively, the "ASSIGNEES") the right, and obligation, to purchase an
aggregate of $35,000,000 of the Securities on the terms and conditions set forth
in the Subscription Agreement (except as explicitly modified hereby), as
Purchasers under the Subscription Agreement. The Assignees acknowledge that
their investment will be required to be made on the Closing Date, simultaneously
with the investments being made by the Investors. The Assignees shall become
"Purchasers" under the Subscription Agreement and "Investors" under the
Shareholders Agreement (solely for purposes of Sections 3.4 and 5.3 and Article
IV thereof and the provisions implementing the provisions described in paragraph
6(b) below); PROVIDED that:

                  (i) Warburg and H&F shall jointly have the sole right (on
         behalf of themselves and all other Purchasers) to make any and all
         determinations with respect to, or to take any and all actions
         necessary to effectuate the provisions of, Section B of the
         Subscription Agreement (including the right to approve any amendment or
         acceleration of, or to waive compliance by Arch with, any of the terms
         thereof), PROVIDED that the consequences of such determinations and
         actions by Warburg and H&F do not apply differently to any Assignee
         than to Warburg and H&F (or, if they apply differently, it is because
         of differences in the treatment of Warburg and H&F as opposed to other
         Purchasers existing in the Subscription Agreement (as modified by this
         Agreement) and such differences are not made more adverse to any
         Assignee or more favorable to Warburg and H&F as a result of such
         determination or action);

                  (ii) Warburg and H&F shall have the sole right to determine
         whether each condition for the Purchasers contained in Section C of the
         Subscription Agreement is satisfied;

                  (iii) the failure of the conditions set forth in Section C.2
         of the Subscription Agreement due to any breach by any Assignee of any
         representation, warranty or covenant shall not affect the obligation of
         the Company to sell the Securities on the Closing Date to either
         Warburg or H&F;

                  (iv) the Assignees shall be subject to Section D.1 and D.2 of
         the Subscription Agreement, including the covenants thereunder;

                  (v) Assignees shall have no rights (including no right to
         consent to any action proposed to be taken by Arch under, or any right
         to waive compliance by Arch with, any covenant or agreement) as a
         "Purchaser" under Section D.4 of the Subscrip-

<Page>
                                      -3-

         tion Agreement, it being acknowledged that each Assignee shall,
         however, have the obligations of a "Purchaser" under Sections D.4(d),
         (g) and (i) thereof; PROVIDED that any information provided to the
         Company pursuant to Section D.4(g) shall be held confidentially and not
         used for any purpose other than as set forth in Section D.4(g);

                  (vi) no Assignee shall be considered an "original signatory"
         to the Subscription Agreement for purposes of Section E.6 thereof,
         PROVIDED that no amendment, modification or waiver of Section E of the
         Subscription Agreement shall affect any Assignee differently than
         Warburg and H&F (or, if they apply differently, it is because of
         differences in the treatment of Warburg and H&F as opposed to other
         Purchasers existing in the Subscription Agreement (as modified by this
         Agreement) and such differences are not made more adverse to any
         Assignee or more favorable to Warburg and H&F as a result of such
         determination or action);

                  (vii) no consent of any Assignee shall be required to effect
         any modification or amendment to the Subscription Agreement (including,
         without limitation, Schedules A and B, and Exhibits I, II and III
         thereto), unless such amendment or modification affects an Assignee
         differently than Warburg and H&F (or, if they apply differently, it is
         because of differences in the treatment of Warburg and H&F as opposed
         to other Purchasers existing in the Subscription Agreement (as modified
         by this Agreement) and such differences are not made more adverse to
         any Assignee or more favorable to Warburg and H&F as a result of such
         determination or action);

                  (viii) the Assignees shall have no rights under Section F.2,
         and no right to assign under Section F.4, of the Subscription
         Agreement; and

                  (ix) for the avoidance of doubt, the Assignees shall become
         parties to the Shareholders Agreement as "Investors" solely for
         purposes of Sections 3.4 and 5.3 and Article IV thereof and the
         provisions thereof implementing the provisions of paragraph 6(b) below;
         it being further understood that Warburg and H&F can consent on behalf
         of all other Investors to (A) any amendment or modification whatsoever
         of the Sections of the Shareholders Agreement that do not apply to any
         Assignee and (B) any amendment or modification of the Sections of the
         Shareholders Agreement that do apply to any Assignee, so long as in the
         case of clause (B) such amendment or modification does not affect any
         Assignee differently than Warburg and H&F (or, if they apply
         differently, it is because of differences in the treatment of Warburg
         and H&F as opposed to other Purchasers existing in the Subscription
         Agreement or the Shareholders Agreement (as modified by this Agreement)
         and such differences are not made more adverse to any Assignee or more
         favorable to Warburg and H&F as a result of such determination or
         action).

<Page>
                                      -4-

                  2. TERMINATION OF MARSH BOARD OBSERVER RIGHTS. The parties
acknowledge that the rights of Marsh & McLennan Risk Capital Holdings, Ltd.
("MARSH") under Section 5(g) of the Amended and Restated Subscription Agreement
dated as of June 28, 1995 (the "1995 MARSH SUBSCRIPTION AGREEMENT") by and
between Arch and Marsh, as amended by paragraph 2 of the Amendment to Amended
and Restated Subscription Agreement dated as of October 31, 2000 by and between
Arch and Marsh, have been terminated.

                  3. DESIGNATION OF TRIDENT DIRECTOR; REPORTS. The parties
acknowledge that all rights of The Trident Partnership, L.P. ("TRIDENT I") under
Section 5(b) of the Amended and Restated Subscription Agreement dated as of June
28, 1995 (the "1995 TRIDENT SUBSCRIPTION AGREEMENT") between Arch and Trident I
have been terminated. For so long as Trident I owns any equity interest in Arch,
Arch agrees furnish to Trident I a copy of its annual and quarterly reports
filed under the Securities Exchange Act of 1934.

                  4. CAPITAL COMMITMENT TO TRIDENT II. Arch is hereby released
from any obligation (pursuant to the Trident II partnership agreement or
otherwise) to make any additional capital contributions to Trident II; in
respect of (i) any investment made by Trident II on or after the date hereof or
(ii) the expenses relating to any such investment; PROVIDED that Arch shall
remain committed to fund its portion (equal to $4,662,388.79) of the outstanding
capital call with respect to AXIS Specialty Limited. This release shall be
without any penalty, forfeiture of rights or other adverse consequence to Arch
or Arch's investment in Trident II, which shall continue with respect to Arch's
interest in all investments of Trident II existing as of the date hereof and the
AXIS investment. For the avoidance of doubt, Arch shall be entitled to its share
of profits, losses and distributions, and be obligated for its share of
management fees and partnership expenses, with respect to Arch's interest in all
investments of Trident II existing as of the date hereof and the Axis
investment. Subject to the foregoing, Arch shall continue to be a Trident II
limited partner and be subject to the rights and obligations of limited
partners, including the indemnification provisions. Upon the Closing Date, Arch
and Trident II shall enter into an appropriate amendment to the Trident II
partnership agreement to reflect the foregoing.

                  5. EXCHANGE/CANCELLATION OF MARSH'S WARRANTS. Effective upon
the Closing Date, all of Marsh's 905,397 Class A Warrants of the Company shall
be canceled in exchange for the issuance by Arch of 140,380 Common Shares.
Effective upon the Closing Date, all of Marsh's 1,770,601 Class B Warrants of
the Company shall be canceled in exchange for the payment by Arch of cash equal
to $7.50 per Class B Warrant (such price aggregating $13,279,507.50). On the
Closing Date, Marsh agrees to deliver to the Company all certificates
representing such Class A Warrants and Class B Warrants (or a certificate of
loss and related appropriate document), and the Company shall deliver the
certificate(s), registered in the name of Marsh, representing the Common Shares
issued to Marsh in exchange for its Class A Warrants. For the avoidance of
doubt, any cancellation or exchange of Class B War-

<Page>
                                      -5-

rants made pursuant to the terms of this Section 5 shall have no effect on any
amount that may become payable to the Purchasers under Section B.2 of the
Subscription Agreement.

                  6. REGISTRATION; TAG-ALONG; TAKE-ALONG. (a) For the avoidance
of doubt, the parties acknowledge that this Agreement does not affect the rights
of Marsh under Section 6 (Registration Rights) of the 1995 Marsh Subscription
Agreement or of Trident I under Section 6 (Registration Rights) of the 1995
Trident Subscription Agreement.

                  (b) Arch, the Purchasers and the Assignees also agree that the
Shareholders Agreement will provide that:

                  (i) if any Assignee exercises its right under Section 4.3
         thereof, any cutback pursuant to Section 4.4 thereof will treat the
         Assignees at least as favorably as Warburg and H&F (I.E., the Assignees
         will have priority under clause (b), and not under clause (c),
         thereof);

                  (ii) each Assignee will have the rights of a Tag-Along
         Investor under Section 5.1 thereof to participate ratably on the basis
         of securities owned in a Third Party Sale (excluding any sale or
         distribution described in the last sentence of Section 5.1 of the
         Shareholders Agreement) on the same terms as the Selling Investor (but,
         for the avoidance of doubt, not have the obligations of a Selling
         Investor under Section 5.1 thereof); PROVIDED that such Assignee shall
         only be responsible for its pro rata portion of any indemnification
         (except in respect of representations specifically relating to such
         Assignee);

                  (iii) in the event of a Third Party Sale (excluding any sale
         or distribution described in the last sentence of Section 5.1 of the
         Shareholders Agreement), the Selling Investor will have the right to
         require each Assignee to participate ratably on the basis of securities
         owned in such Third Party Sale on the same terms as the Selling
         Investor; PROVIDED that such Assignee shall only be responsible for its
         pro rata portion of any indemnification (except in respect of
         representations specifically relating to such Assignee).

                  (iv) each Assignee shall be subject to the restrictions of
         Section 5.2 of the Shareholders Agreement with respect to the
         Securities acquired by it under the Subscription Agreement and any
         securities acquired in respect thereof, to the same extent that Warburg
         and H&F are restricted with respect to the Securities acquired by them
         under the Subscription Agreement and any securities acquired in respect
         thereof.

"Tag-Along Investor," "Third Party Sale and "Selling Investor" have the meanings
given to them in the Shareholders Agreement and to the extent necessary the term
"Tag-Along Investor" shall be deemed to include more than one party.

<Page>
                                      -6-

                  7. FURTHER ASSURANCES. Subject to the terms and conditions of
this Agreement, each of the parties hereto agrees to use its reasonable best
efforts to take, or cause to be taken, all action, and to do, or cause to be
done, all things necessary or desirable under applicable legal requirements, to
consummate and make effective the transactions contemplated by this Agreement.
If at any time after the Closing Date, any further action is necessary or
desirable to carry out the purposes of this Agreement, the parties hereto shall
use their reasonable best efforts to take or cause to be taken all such
necessary or desirable action and execute, and deliver and file, or cause to be
executed, delivered and filed, all necessary or desirable documentation. Each of
Trident I, Trident II, Marsh and the Co-Investment Funds agree (to the full
extent of their current or future ownership of securities of Arch) to vote in
favor of all matters to be submitted to shareholders of Arch in connection with
the foregoing or the transactions contemplated by the Subscription Agreement
(and the grants of any shares or options contemplated thereby or in connection
therewith). Each of the parties will consult with each other with respect to the
issuance of any press release or public announcement with respect to the
foregoing.

                  8. NOTICES. All notices or other communications given or made
hereunder shall be validly given or made if in writing and delivered by
facsimile transmission or in person at, or mailed by registered or certified
mail, return receipt requested, postage prepaid, to, the addresses (and shall be
deemed effective at the time of receipt thereof):

                  (i)      If to Arch:

                           Arch Capital Group Ltd.
                           20 Horseneck Lane
                           Greenwich, CT  06830
                           Attention:  Peter Appel, President and Chief
                                       Executive Officer
                           Facsimile:  (203) 861-7240

<Page>
                                      -7-

                  (ii)     If to Trident I, Trident II, Marsh or the Employee
                           Co-Investment Funds, to it at:

                           1166 Avenue of the Americas
                           New York, New York  10036
                           Attention:  Mark Dallara
                           Facsimile:  (212) 345-5627

                           and

                           c/o Marsh & McLennan Capital, Inc.
                           20 Horseneck Lane
                           Greenwich, CT  06830
                           Attention:  David Wermuth
                           Facsimile:  (203) 862-2925

or to such other address as the party to whom notice is to be given may have
previously furnished notice in writing to the other in the manner set forth
above. A notice hereunder shall not be deemed given until copies thereof are
given as contemplated above. Notices to all other parties hereto shall be given
in accordance with the Subscription Agreement.

                  9. ENTIRE AGREEMENT; AMENDMENT. This Agreement contains all of
the terms agreed upon by the parties with respect to the subject matter hereof.
This Agreement may be amended or the provisions thereof waived only by a written
instrument signed by the party against whom enforcement of any waiver, change,
modification, extension or discharge is sought.

                  10. HEADINGS. The headings of the sections of this Agreement
are inserted for convenience only and shall not constitute a part hereof.

                  11. ASSIGNMENT. This Agreement and all of the provisions
hereof shall be binding upon and inure to the benefit of the parties hereto and
their respective permitted assigns, but neither this Agreement nor any of the
rights, interests or obligations hereunder shall be assigned by any party
without the prior written consent of the other party; PROVIDED that this
Agreement may be assigned by a Purchaser consistent with an assignment in
accordance with Section F.4 of the Subscription Agreement.

                  12. SEVERABILITY. In the event that any provision or any part
of this Agreement is held to be illegal, invalid or unenforceable, such
illegality, invalidity or unenforceability shall not effect the validity or
enforceability of any other provision or part thereof.

<Page>
                                      -8-

                  13. GOVERNING LAW. This Agreement shall be governed in all
respects, including validity, interpretation and effect, by the substantive laws
of the State of New York, without giving effect to principles of conflicts of
laws.

                  14. COUNTERPARTS. This Agreement and any instrument delivered
in connection herewith may be executed in any number of counterparts with the
same effect as if the signatures on all counterparts are upon the same
instrument.

                            [Signature pages follow]

<Page>
                                      -9-

                  Please confirm that the foregoing is in accordance with your
understanding by signing and returning to us the duplicate enclosed copy of this
Agreement.

                                             Very truly yours,

                                             ARCH CAPITAL GROUP LTD.

                                             By: /s/ Peter A. Appel
                                                --------------------------------
                                             Name: Peter A. Appel
                                             Title: President and CEO

Agreed to and Accepted
As of the Date First Above Written:

THE TRIDENT PARTNERSHIP, L.P.

By: /s/ Martine Purssell
   ----------------------------------------------
Name: Martine Purssell
Title: Asst. Secretary, Trident Corp. General Partner

TRIDENT II, L.P.

By: MMC Capital, Inc., as Manager

By: /s/ David J. Wermuth
   ----------------------------------------------
Name: David J. Wermuth
Title: Principal

<Page>
                                      -10-

MARSH & MCLENNAN RISK
CAPITAL HOLDINGS, LTD.

By: /s/ Mark J. Dallara
   ----------------------------------------------
Name: Mark J. Dallara
Title: Assistant Secretary

MARSH & MCLENNAN CAPITAL
PROFESSIONALS FUND, L.P.

By: MMC Capital, Inc., as Manager

By: /s/ David J. Wermuth
   ----------------------------------------------
Name: David J. Wermuth
Title: Principal

MARSH & MCLENNAN EMPLOYEES'
SECURITIES COMPANY, L.P.

By: MMC Capital, Inc., as Manager

By: /s/ David J. Wermuth
   ----------------------------------------------
Name: David J. Wermuth
Title: Principal
<Page>
                                      -11-

HFCP IV (BERMUDA), L.P.

By:    H&F Investors IV, LLC,
       its General Partner

       By:    H&F Investors III, Inc.
              its Manager

By: /s/ John L. Bunce, Jr.
   ----------------------------------------------
Name: John L. Bunce, Jr.
Title: Vice President

WARBURG PINCUS PRIVATE EQUITY VIII, L.P.

WARBURG PINCUS INTERNATIONAL PARTNERS, L.P.

WARBURG PINCUS NETHERLANDS INTERNATIONAL PARTNERS I, C.V.

WARBURG PINCUS NETHERLANDS INTERNATIONAL PARTNERS II, C.V.

       By:    Warburg, Pincus & Co.,
              its General Partner

By: /s/ Kewsong Lee
   ----------------------------------------------
Name: Kewsong Lee
Title: Partner

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