Document:

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                        MANAGEMENT SUBSCRIPTION AGREEMENT

       This Management Subscription Agreement (this "AGREEMENT") is made as of
October 24, 2001 by and between Arch Capital Group Ltd., a company organized
under the laws of Bermuda (the "COMPANY"), and each of the Purchasers named
below (each, a "PURCHASER" and, collectively, the "PURCHASERS"), in connection
with the purchase by each Purchaser of the Securities (as defined below).

       WHEREAS, the Company has entered into a subscription agreement dated as
of even date herewith with the purchasers named therein (the "WARBURG/H&F
AGREEMENT"), a true and correct copy of which has been provided to the
Purchasers. Reference is made throughout this Agreement to certain terms,
conditions and other provisions of the Warburg/H&F Agreement. The terms,
conditions and other provisions so referenced are incorporated into and made a
part of this Agreement as if such terms, conditions and other provisions were
set forth herein. Certain capitalized terms used herein, but not defined, are
defined, and shall have the meanings ascribed thereto, in the Warburg/H&F
Agreement (including SCHEDULE A thereto).

       For good and valid consideration, the receipt of which is hereby
acknowledged, the Company and each of the Purchasers agree as follows:

A.     SUBSCRIPTION AND PURCHASE OF SECURITIES

       1. AGREEMENT TO PURCHASE. Subject to satisfaction of the conditions set
forth in Section B below (or incorporated therein by reference), each Purchaser,
severally and not jointly, hereby irrevocably subscribes for and agrees to
purchase, for the aggregate purchase price set forth below the name of such
Purchaser on the signature page hereto (such Purchaser's "TOTAL PURCHASE
PRICE"), series A convertible preference shares (the "PREFERENCE SHARES") and
class A warrants (such warrants issued hereunder, the "WARRANTS" and together
with the Preference Shares, the "SECURITIES") of the Company. The Preference
Shares will have the rights and privileges set forth in the form of Certificate
of Designations attached to the Warburg/H&F Agreement as EXHIBIT I (the
"CERTIFICATE"). The Preference Shares will be convertible, on the terms and
conditions set forth in the Certificate, into Common Shares (such shares, the
"CONVERSION SHARES") or, in the circumstances set forth in Section D hereof (or
incorporated therein by reference), common shares of Newco. The form of the
Warrants is attached to the Warburg/H&F Agreement as EXHIBIT II. The Warrants
will be exercisable, on the terms and conditions thereof for Common Shares (such
shares, the "WARRANT SHARES").

       2. NUMBER OF SECURITIES PURCHASED. The number of Preference Shares to be
purchased by each Purchaser shall be equal to such Purchaser's Total Purchase
Price divided by the Estimated Per Share Price. The number of Warrants to be
purchased by each Purchaser shall be equal to (a) the Adjusted Warrant Amount
times (b) the number of Com-

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                                      -2-

mon Shares issuable as of the date hereof upon exercise of all class A warrants
outstanding on the date hereof (which is 2,531,079) divided by (c) the number of
Common Shares outstanding as of June 30, 2001 (which is 12,863,079).

       3. ADJUSTMENTS. If the transactions contemplated by this Agreement and
the Warburg/H&F Agreement, or options granted to management concurrently
herewith, trigger an anti-dilution adjustment under existing class A warrants,
the number of Warrants purchased by each Purchaser hereunder shall be adjusted
upward to reflect the greater number of shares issuable upon exercise of
outstanding class A warrants as a result of such anti-dilution adjustment. In
the event that there is an adjustment pursuant to Section B.1, B.2 or B.3 of the
Warburg/H&F Agreement, there shall be a similar adjustment hereunder, it being
understood that the Purchasers' rights under this sentence are subject to
Section C.1.g of this Agreement.

       4. CLOSING DATE. Subject to the terms and conditions hereof, the purchase
and sale of the Securities shall occur at the Closing Date (as determined
pursuant to the Warburg/H&F Agreement).

       5. DELIVERIES. As of the close of business on the business day
immediately preceding the Closing Date, the Company shall advise the Purchasers
of the Estimated Per Share Price. On the Closing Date, (a) each Purchaser shall
pay its Total Purchase Price by wire transfer of immediately available funds to
the account of the Company designated by the Company and (b) the Company shall
deliver to such Purchaser certificates for the Securities purchased by such
Purchaser, registered in the name of such Purchaser or its designee.

B.     CONDITIONS PRECEDENT TO SALE OF PREFERENCE
       SHARES ON THE CLOSING DATE

       1. MUTUAL CONDITIONS. The obligation of the Company to sell, and of each
Purchaser to buy, the Securities on the Closing Date, is subject to the
satisfaction, or waiver by the parties hereto, of the following conditions:

              (a) The purchase and sale of securities pursuant to the
       Warburg/H&F Agreement shall have occurred, or shall occur substantially
       concurrently with the purchase and sale hereunder.

              (b) There shall not be in effect an order or injunction of a court
       of competent jurisdiction prohibiting the consummation of the sale and
       purchase of the Securities hereunder that are to be purchased on the
       Closing Date.

              (c) The Company and the Purchasers shall have executed and
       delivered the Shareholders Agreement, pursuant to which the Purchasers
       shall have the rights of,

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                                      -3-

       and be subject to the obligations of, an "Investor" solely for purposes
       of Article IV and Sections 3.4 and 5.3 thereof and the provisions
       implementing Section C.1.f hereof.

       2. CONDITIONS OF THE COMPANY. The obligation of the Company to sell the
Securities on the Closing Date is subject to the satisfaction, or waiver by the
Company, of the following conditions:

              (a) The representations and warranties made by each Purchaser in
       this Agreement shall be true and accurate in all material respects as of
       the Closing Date.

              (b) Each Purchaser shall have complied with and performed all
       agreements and covenants to be complied with or performed by it in all
       material respects at or prior to the Closing Date.

C.     REPRESENTATIONS, WARRANTIES AND AGREEMENTS

       1. PURCHASER ACKNOWLEDGMENTS. Each Purchaser, severally and not jointly,
understands, acknowledges and hereby covenants and agrees with the Company as
follows:

              (a) Subject to the terms and conditions of this Agreement, such
       Purchaser's agreement to purchase Securities hereunder is and shall be
       irrevocable.

              (b) The offering and sale of the Securities is intended to be
       exempt from registration under the United States Securities Act of 1933,
       as amended (the "ACT"), by virtue of Section 4(2) of the Act. The
       Securities, the Conversion Shares and the Warrant Shares have not been
       registered under the Act. Except to the extent set forth in the
       Shareholders Agreement, the Company is under no obligation to register
       the Securities, the Conversion Shares or the Warrant Shares or to assist
       such Purchaser in complying with any exemption from registration.

              (c) There is no existing public or other market for the
       Securities, and it is not expected that any such market will develop.
       There can be no assurance that such Purchaser will be able to sell or
       dispose of its Securities. Without limiting the generality of the
       foregoing, in order not to jeopardize the offering's exempt status under
       the Act, a transferee of such Securities may, among other things, be
       required to fulfill the investor suitability requirements thereunder.

              (d) All certificates issued for the Securities, the Conversion
       Shares and the Warrant Shares will bear the legend set forth in Section
       D.1.d of the Warburg/H&F Agreement.

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                                      -4-

              (e) Prior to the earlier of the Shareholders Meeting and the four
       month anniversary of the Closing Date, the Securities, Conversion Shares
       and the Warrant Shares may not be sold, transferred or otherwise disposed
       of, directly or indirectly, without approval of the Transaction Committee
       (excluding Robert Clements or Peter Appel in the case of a sale, transfer
       or other disposition by Robert Clements or Peter Appel, as the case may
       be).

              (f) Each Purchaser shall be subject to the restrictions of Section
       5.2 of the Shareholders Agreement with respect to the Securities acquired
       by it under this 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 Warburg/H&F
       Agreement and any securities acquired in respect thereof.

              (g) The terms of the purchase of the Securities hereunder shall,
       except as explicitly set forth herein, be on substantially the same terms
       and conditions set forth in the Warburg/H&F Agreement as it may be
       amended, modified, interpreted or implemented in the future. No consent
       of any Purchaser hereunder shall be required with respect to any
       amendment, modification, interpretation or implementation of the
       Warburg/H&F Agreement unless the consequences of such modification,
       amendment or interpretation of, or such action or determination made by
       Warburg and H&F implementing the terms of, or such waiver of any rights
       by Warburg and H&F under, the Warburg/H&F Agreement applies differently
       to any Purchaser than to Warburg and H&F (or, if they apply differently,
       it is because of differences in the treatment of Warburg and H&F under
       the Warburg/H&F Agreement (as opposed to other Purchasers under the
       Warburg/H&F Agreement or this Agreement) and such differences are not
       made more adverse to any Purchaser, or more favorable to Warburg and H&F,
       as a result of such modification, amendment or interpretation, such
       action or determination, or such waiver). Without limiting the generality
       of, but subject to, the foregoing, and for the avoidance of doubt, the
       Purchasers acknowledge and agree:

                     (i) Warburg and H&F shall jointly have the sole right (on
              behalf of themselves and all Purchasers under the Warburg/H&F
              Agreement and this Agreement) 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 Warburg/H&F
              Subscription Agreement (including the right to approve any
              amendment or acceleration of, or to waive compliance by Arch with,
              any of the terms thereof), which decisions shall apply with equal
              force to Section A.3 of this Agreement; PROVIDED that the
              consequences of such determinations and actions by Warburg and H&F
              do not apply differently to any Purchaser 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
              under the

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                                      -5-

              Warburg/H&F Agreement or this Agreement and such differences are
              not made more adverse to any Purchaser or more favorable to
              Warburg and H&F as a result of such determination or action);

                     (ii) the Purchasers 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 Warburg/H&F
              Agreement, it being acknowledged that each Purchaser shall,
              however, have the obligations of a "Purchaser" under Sections
              D.4(d), (g) and (i) thereof (and which are incorporated herein by
              reference);

                     (iii) no Purchaser shall be considered an "original
              signatory" to the Warburg/H&F Agreement for purposes of Section
              E.6 thereof; PROVIDED that no amendment, modification or waiver of
              Section E of the Warburg/H&F Agreement shall affect any Purchaser
              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 under the Warburg/H&F Agreement or
              this Agreement and such differences are not made more adverse to
              any Purchaser or more favorable to Warburg and H&F as a result of
              such determination or action);

                     (iv) no consent of any Purchaser shall be required to
              effect any modification or amendment to the Warburg/H&F Agreement
              (including, without limitation, Schedules A and B, and Exhibits I,
              II and III thereto), unless such amendment or modification affects
              a Purchaser 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 under the
              Warburg/H&F Agreement or this Agreement and such differences are
              not made more adverse to any Purchaser or more favorable to
              Warburg and H&F as a result of such determination or action);

                     (v) the Purchasers shall have no rights under Section F.2,
              and no right to assign under Section F.4, of the Warburg/H&F
              Agreement; and

                     (vi) the Purchasers 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
              implementing Section C.1.f hereof; 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 the Purchasers and
              (B) any amendment or modification of the Sections of the
              Shareholders Agreement that do apply to any Purchaser, so long as,
              in the case of clause (B), such amend-

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              ment or modification does not affect any Purchaser 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 under the Warburg/H&F Agreement or the
              Shareholders Agreement, and such differences are not made more
              adverse to any Purchaser, or more favorable to Warburg and H&F as
              a result of such determination or action).

       2. PURCHASER REPRESENTATIONS. Each Purchaser, severally and not jointly,
hereby represents and warrants and covenants to the Company as follows:

              (a) The Securities to be purchased by such Purchaser are being
       purchased for such Purchaser's own account, and not with a view to
       distribution, assignment or resale to others or to fractionalization in
       whole or in part. No other person has or will have a direct or indirect
       beneficial interest in such Securities or any component thereof.

              (b) The financial situation of such Purchaser is such that it can
       afford to bear the economic risk of holding the Securities for an
       indefinite period, and such Purchaser can afford to suffer the complete
       loss of its investment in the Securities. Such Purchaser has (i)
       knowledge and experience in financial and business matters such that it
       is capable of evaluating the risks of the investment in the Securities
       and (ii) carefully reviewed the terms and provisions of this Agreement
       and the terms, conditions and other provisions of the Warburg/H&F
       Agreement incorporated herein by reference and has evaluated the
       restrictions and obligations contained herein.

              (c) This Agreement has been duly authorized, executed and
       delivered by such Purchaser and, assuming due execution and delivery by
       each other party hereto, constitutes a valid and binding obligation of
       such Purchaser enforceable in accordance with its terms.

              (d) Such Purchaser shall hold the Securities subject to, and shall
       have voting rights with respect thereto as specified in, the Company's
       Bye-laws and the Certificate in effect from time to time and shall not
       assign, sell, hypothecate or otherwise transfer the Securities, the
       Conversion Shares or the Warrant Shares other than in accordance with
       applicable law and the provisions with respect thereto in such documents.

              (e) Such Purchaser covenants and agrees to make available to the
       Company and the appropriate insurance regulatory governmental authorities
       all information concerning such Purchaser required to be furnished to
       such governmental authorities in connection with obtaining requisite
       approvals, and further covenants and agrees to

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                                      -7-

       make all filings, and seek to acquire all consents, required by such
       governmental authorities.

              (f) The execution, delivery and performance by such Purchaser of
       this Agreement and the consummation of the transactions contemplated
       hereby do not and will not (i) assuming compliance with the matters
       referred to in Section B.1(a) hereof, violate any provision of any
       applicable law, statute, ordinance, rule, regulation, judgment,
       injunction, order or decree or (ii) violate or result in a default under
       any agreement or other instrument binding upon such Purchaser, except in
       each case as would not reasonably be expected to have, individually or in
       the aggregate, a Material Adverse Effect on such Purchaser.

              (g) Such Purchaser has, or will have prior to the Closing Date,
       sufficient cash or other sources of immediately available funds to enable
       it to make payment of the purchase price for the Securities as required
       hereunder and all related fees and expenses.

D.     RIGHT TO EXCHANGE PREFERENCE SHARES

       The Company hereby agrees to the same terms, covenants and agreements set
forth in Section E of the Warburg/H&F Agreement as if such terms, covenants and
agreements were set forth herein and as if the Purchasers under this Agreement
were substituted for the purchasers under the Warburg/H&F Agreement, it being
understood that the Purchasers' rights under this sentence are subject to
Section C.1.g of this Agreement. For the avoidance of doubt, the minimum
threshold for the initial exchange under such Section shall be Preference Shares
representing a minimum of $150 million in Liquidation Preference held by the
Purchasers under this Agreement and the purchasers under the Warburg/H&F
Agreement, in the aggregate.

E.     ADDITIONAL PROVISIONS

       1. MODIFICATION. This Agreement may not be modified, amended or
supplemented except in writing and signed by the party against whom any
modification, amendment or supplement is sought. No term or condition of this
Agreement may be, or will be deemed to have been, waived except in writing by
the party charged with the waiver. A waiver shall operate only as to the
specific term or condition waived and will not constitute a waiver for the
future or act on anything other than that which is specifically waived. Any
modification, amendment, supplement or waiver to be executed by the Company must
be approved by the Transaction Committee.

       2. NOTICES. Any notice or other communications required or permitted to
be given pursuant to this Agreement shall be in writing and shall be sent by
registered or cer-

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                                      -8-

tified mail, return receipt requested, postage prepaid, by hand delivery
(including courier services), or by facsimile as follows:

                  if to the Company, to:

                         Arch Capital Group Ltd.
                         20 Horseneck Lane
                         Greenwich, CT  06830
                         Attention:  General Counsel
                         Facsimile:  (203) 861-7240

                  with copies to:

                         Cahill Gordon & Reindel
                         80 Pine Street
                         New York, NY  10005
                         Attention:  Immanuel Kohn, Esq.
                         Facsimile:  (212) 269-5420

and if to any Purchaser, at the address set forth on the signature pages hereof
or, with respect to the Company and the Purchasers, to such other person or
address as either party shall specify by like notice to the other party. Any
notice or communication shall be deemed given or made (a) when delivered by
hand, (b) when mailed, three business days after being deposited in the mail,
postage prepaid, sent by certified mail, return receipt requested, and (c) when
sent by facsimile, receipt acknowledged.

       3. SUCCESSORS, ASSIGNS. This Agreement and all of the terms and
provisions hereof shall be binding upon and inure to the benefit of the parties
hereto and their respective successors and assigns; PROVIDED that this Agreement
is not transferable or assignable by any Purchaser (other than to any Affiliate
of such Purchaser) without the Company's consent

       4. GOVERNING LAW. The validity and effects of this Agreement shall be
governed by and construed and enforced in accordance with the laws of the State
of New York.

       5. ENTIRE AGREEMENT. This Agreement and the terms, conditions and other
provisions of the Warburg/H&F Agreement incorporated herein by reference
constitute the entire agreement among the parties hereto and supersedes all
prior agreements, understandings and arrangements, oral or written, among the
parties hereto with respect to the subject matter hereof.

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       6. SEVERABILITY. If any one or more of the provisions contained in this
Agreement shall be held to be invalid, illegal or unenforceable in any respect,
such invalidity, illegality or unenforceability will not affect any other
provision hereof.

       7. COUNTERPARTS. This Agreement may be executed in any number of
counterparts, each of which shall be considered an original and all of which
together shall be deemed to be one and the same instrument.

       8. CURRENCIES. Unless otherwise specifically indicated, all payments and
currency amounts indicated herein refer to and shall be denominated in United
States Dollars. "Dollars" and "$" shall denote United States Dollars.

                            [Signature pages follow]

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                                      S-1

       IN WITNESS WHEREOF, each Purchaser has executed this Agreement as of the
date first above-written.

                                          SOUND VIEW PARTNERS LP

                                          By: Robert Clements,
                                              its General Partner

                                          /s/ Robert Clements
                                          ----------------------------------

Amount Subscribed:  $2.0 million

Notices to:

With copies to:

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                                      S-2

       IN WITNESS WHEREOF, each Purchaser has executed this Agreement as of the
date first above-written.

                                        OTTER CAPITAL LLC

                                        By: John M. Pasquesi,
                                            its Managing Member

                                        /s/ John M. Pasquesi
                                        ------------------------------------

Amount Subscribed:  $7.5 million

Notices to:    Otter Capital LLC
               One Maritime Plaza
               Suite 1200
               San Francisco, CA  94111

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                                      S-3

       IN WITNESS WHEREOF, each Purchaser has executed this Agreement as of the
date first above-written.

                                        /s/ Peter A. Appel
                                        ------------------------------------
                                        Peter A. Appel

Amount Subscribed:  $1.0 million

Notices to:

With copies to:

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                                      S-4

       IN WITNESS WHEREOF, each Purchaser has executed this Agreement as of the
date first above-written.

                                        /s/ Paul B. Ingrey
                                        ------------------------------------
                                        Paul B. Ingrey

Amount Subscribed:  $2.0 million

Notices to:

With copies to:

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                                      S-5

       IN WITNESS WHEREOF, each Purchaser has executed this Agreement as of the
date first above-written.

                                        /s/ Dwight R. Evans
                                        ------------------------------------
                                        Dwight R. Evans

Amount Subscribed:  $400,000

Notices to:

With copies to:

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                                      S-6

       IN WITNESS WHEREOF, each Purchaser has executed this Agreement as of the
date first above-written.

                                        /s/ Marc Grandisson
                                        ------------------------------------
                                        Marc Grandisson

Amount Subscribed:  $250,000

Notices to:

With copies to:

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                                      S-7

Accepted and agreed to as of the date first above-written.

ARCH CAPITAL GROUP LTD.

By: /s/ Louis Petrillo
    -------------------------------------
    Name:  Louis Petrillo
    Title: Senior Vice President
           and General Counsel<Page>

                                                                    EXHIBIT 10.4

                              EMPLOYMENT AGREEMENT

      EMPLOYMENT AGREEMENT ("AGREEMENT") dated as of October 23, 2001 between
Arch Capital Group Ltd., a Bermuda corporation ("PARENT"), Arch Reinsurance
Ltd., a Bermuda corporation (the "COMPANY" and, together with Parent,
collectively referred to herein as the "COMPANIES"), and Paul B. Ingrey (the
"Executive").

      The parties hereto agree as follows:

                                    ARTICLE 1

                                   DEFINITIONS

      SECTION 1.01. DEFINITIONS. For purposes of this Agreement, the following
terms have the meanings set forth below:

      "BASE SALARY" has the meaning set forth in Section 4.01.

      "CAUSE" means (a) theft or embezzlement by the Executive with respect to
the Companies or their Subsidiaries; (b) malfeasance or gross negligence in the
performance of the Executive's duties; (c) the commission by the Executive of
any felony or any crime involving moral turpitude; (d) willful or prolonged
absence from work by the Executive (other than by reason of disability due to
physical or mental illness) or failure, neglect or refusal by the Executive to
perform his duties and responsibilities without the same being corrected within
ten (10) days after being given written notice thereof; (e) continued and
habitual use of alcohol by the Executive to an extent which materially impairs
the Executive's performance of his duties without the same being corrected
within ten (10) days after being given written notice thereof; (f) the
Executive's use of illegal drugs without the same being corrected within ten
(10) days after being given written notice thereof; (g) the Executive's failure
to use his best efforts to obtain, maintain or renew the work permit described
in Section 3.02 below without the same being corrected within ten (10) days
after being given written notice thereof; or (h) the material breach by the
Executive of any of the covenants contained in this Agreement.

      "CONFIDENTIAL INFORMATION" means information that is not generally known
to the public and that was or is used, developed or obtained by the Companies or
their Subsidiaries in connection with their business. It shall not include
information (a) required to be disclosed by court or administrative order, (b)
lawfully obtainable from other sources or which is in the public domain through
no fault of the Executive; or (c) the disclosure of which is consented to in
writing by the Companies.

      "DATE OF TERMINATION" has the meaning set forth in Section 5.06.

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                                      -2-

      "EMPLOYMENT PERIOD" has the meaning set forth in Section 2.01.

      "GOOD REASON" means, without the Executive's written consent, (a) the
material diminution of any material duties or responsibilities of the Executive
without the same being corrected within ten (10) days after being given written
notice thereof; (b) a material reduction in the Executive's Base Salary; or (c)
the Company giving written notice pursuant to Section 5.01 of its intention not
to extend the Employment Period.

      "INTELLECTUAL PROPERTY" has the meaning set forth in Section 7.01.

      "NOTICE OF TERMINATION" has the meaning set forth in Section 5.05.

      "NONCOMPETITION PERIOD" has the meaning set forth in Section 9.01.

      "PERSON" means an individual, a partnership, a corporation, a limited
liability company, an association, a joint stock company, an estate, a trust, a
joint venture, an unincorporated organization or a governmental entity or any
department, agency or political subdivision thereof.

      "PERMANENT DISABILITY" means those circumstances where the Executive is
unable to continue to perform the usual customary duties of his assigned job or
as otherwise assigned in accordance with the provisions of this Agreement for a
period of six (6) months in any twelve (12) month period because of physical,
mental or emotional incapacity resulting from injury, sickness or disease. Any
questions as to the existence of a Permanent Disability shall be determined by a
qualified, independent physician selected by the Companies and approved by the
Executive (which approval shall not be unreasonably withheld). The determination
of any such physician shall be final and conclusive for all purposes of this
Agreement.

      "REIMBURSABLE EXPENSES" has the meaning set forth in Section 4.04.

      "SUBSIDIARY" or "SUBSIDIARIES" means, with respect to any Person, any
corporation, partnership, limited liability company, association or other
business entity of which (a) if a corporation, fifty (50) percent or more of the
total voting power of shares of stock entitled (without regard to the occurrence
of any contingency) to vote in the election of directors, managers or trustees
thereof is at the time owned or controlled, directly or indirectly, by that
Person or one or more of the other Subsidiaries of that Person or combination
thereof; or (b) if a partnership, limited liability company, association or
other business entity, fifty (50) percent or more of the partnership or other
similar ownership interest thereof is at the time owned or controlled, directly
or indirectly, by any Person or one or more Subsidiaries of that Person or a
combination thereof. For purposes of this definition, a Person or Persons will
be deemed to have a fifty (50) percent or more ownership interest in a
partnership, limited liability company, association or other business entity if
such Person or Persons are allocated fifty (50)

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                                      -3-

percent or more of partnership, limited liability company, association or other
business entity gains or losses or control the managing director or member or
general partner of such partnership, limited liability company, association or
other business entity.

                                    ARTICLE 2

                                   EMPLOYMENT

      SECTION 2.01. EMPLOYMENT. The Company shall employ the Executive, and the
Executive shall accept employment with the Company, upon the terms and
conditions set forth in this Agreement for the period beginning on the date the
work permit described in Section 3.02 is issued to the Executive (the "Work
Permit Date") and ending as provided in Section 5.01. For the period beginning
on the date hereof and ending on the Work Permit Date, Parent shall employ the
Executive, and the Executive hereby accepts employment with Parent for such
period. The period beginning on the date hereof and ending as provided in
Section 5.01 is referred to herein as the "Employment Period."

                                    ARTICLE 3

                               POSITION AND DUTIES

      SECTION 3.01. POSITION AND DUTIES. Effective on the Work Permit Date, the
Executive shall serve as Chairman and Chief Executive Officer of the Company and
shall have such responsibilities, powers and duties as may from time to time be
prescribed by the Board of Directors of the Company; PROVIDED that such
responsibilities, powers and duties are substantially consistent with those
customarily assigned to individuals serving in such position at comparable
companies or as may be reasonably required by the conduct of the business of the
Company. Prior to the Work Permit Date the Executive shall be employed by Parent
and shall only provide services reasonably required in connection with obtaining
financing for Parent. During the Employment Period the Executive shall devote
substantially all of his working time and efforts to the business and affairs of
the Companies. The parties hereto anticipate that the Executive's working time
hereunder will be approximately three (3) days per week. The Executive shall not
directly or indirectly render any services of a business, commercial or
professional nature to any other person or for-profit organization not related
to the business of the Companies or their Subsidiaries, whether for compensation
or otherwise, without prior written consent of the Parent. Notwithstanding the
foregoing, the Executive may continue to serve as a non-employee director of
Fairfax Financial Holdings and its subsidiary, Odyssey Reinsurance so long as
such service does not materially interfere with the performance of the
Executive's duties hereunder.

      SECTION 3.02. WORK PERMITS. The Executive shall use his best efforts to
obtain, maintain and renew a suitable (for the purposes of the Executive's
contemplated employment

<Page>
                                      -4-

by the Company) work permit by the Bermuda government authorities and any other
permits required by any Bermuda government authority. The Company shall be
responsible for permit fees.

      SECTION 3.03. WORK LOCATION. While employed by the Company hereunder, the
Executive shall perform his duties (when not traveling or engaged elsewhere
outside the United States in the performance of his duties) at the offices of
the Company in Bermuda. The Executive shall travel to such places outside the
United States on the business of the Company in such manner and on such
occasions as the Company may from time to time reasonably require.

                                    ARTICLE 4

                            BASE SALARY AND BENEFITS

      SECTION 4.01. BASE SALARY. During the Employment Period, the Executive's
base salary will be $750,000 per annum (the "BASE SALARY"). The Base Salary will
be payable bi-monthly on the 15th and last working day of each month in arrears.
Annually during the Employment Period the Board of Directors of the Company
shall review with the Executive his job performance and compensation, and if
deemed appropriate by the Board of Directors of the Company, in its discretion,
the Executive's Base Salary may be increased. Normal hours of employment at the
Company are 8:30 a.m. to 5:00 p.m., Monday to Friday. The Executive's salary has
been computed to reflect that his regular duties are likely, from time to time,
to require more than the normal hours per week and the Executive shall not be
entitled to receive any additional remuneration for work outside normal hours.

      SECTION 4.02. BONUSES. In addition to the Base Salary, the Executive shall
be eligible to participate in an annual bonus plan on terms set forth from time
to time by the Board of Directors of the Company; PROVIDED, HOWEVER, that the
Executive's target annual bonus will be 100% of his Base Salary.

      SECTION 4.03. BENEFITS. In addition to the Base Salary, and any bonuses
payable to the Executive pursuant to this Agreement, the Executive shall be
entitled to the following benefits during the Employment Period:

            (a) such major medical, life insurance and disability insurance
      coverage as is, or may during the Employment Period, be provided generally
      for other senior executive officers of the Company as set forth from time
      to time in the applicable plan documents;

            (b) in addition to the usual public holidays and eight (8) paid days
      off for sick leave, a maximum of four (4) weeks of paid vacation annually
      during the term of

<Page>
                                      -5-

      the Employment Period (Section 11 of the Bermuda Employment Act 2000 shall
      otherwise not apply to the Executive's employment hereunder); and

            (c) benefits under any plan or arrangement available generally for
      the senior executive officers of the Company, subject to and consistent
      with the terms and conditions and overall administration of such plans as
      set forth from time to time in the applicable plan documents.

      SECTION 4.04. EXPENSES. The Company shall reimburse the Executive for all
reasonable expenses incurred by him in the course of performing his duties under
this Agreement which are consistent with the Company's policies in effect from
time to time with respect to travel, entertainment and other business expenses,
("REIMBURSABLE EXPENSES"), subject to the Companies' requirements with respect
to reporting and documentation of expenses.

      SECTION 4.05. STOCK OPTIONS RESTRICTED STOCK AND STOCK PURCHASE. On the
date hereof, Parent shall grant to the Executive an option to acquire 417,000
shares of Parent's common stock at an exercise price of $20.00 per share. The
other terms of the stock option shall be as set forth in the form of Stock
Option Agreement attached hereto as Exhibit A. On the date hereof, Parent shall
also grant to the Executive 417,000 shares of restricted common stock of Parent
on the terms set forth in the form of Restricted Stock Agreement attached hereto
as Exhibit B. The stock option and restricted stock awards provided for this
Section 4.05 are made as an inducement essential to the Executive's entering
into the Agreement.

                                    ARTICLE 5

                              TERM AND TERMINATION

      SECTION 5.01. TERM. The Employment Period will terminate on the third
anniversary of the date hereof; PROVIDED THAT (a) the Employment Period shall
terminate prior to such date upon the Executive's death or Permanent Disability,
(b) the Employment Period may be terminated by the Companies for any reason
prior to such date, and (c) the Employment Period may be terminated by the
Executive at any time prior to such date, if such termination shall be for Good
Reason. In addition, this Agreement will be automatically extended on the same
terms and conditions for successive one year periods following the original
three (3) year term until either the Companies or the Executive, at least sixty
(60) days prior to the expiration of the original term or any extended term,
shall give written notice of their intention not to renew the Agreement.

      SECTION 5.02. UNJUSTIFIED TERMINATION. Except as otherwise provided in
Section 5.03, if the Employment Period shall be terminated prior to the
expiration of the third anniversary of the date hereof (or the extension of the
Employment Period pursuant to Section 5.01) by the Executive for Good Reason or
by the Companies not for Cause (collectively, an "UN-

<Page>
                                      -6-

JUSTIFIED TERMINATION") (it being understood that a termination (a) for Cause,
(b) as a result of the Executive's resignation or leaving his employment other
than for Good Reason, or (c) as a result of the death or Permanent Disability of
the Executive shall not constitute an Unjustified Termination), the Executive
shall be paid solely (except as provided in Section 5.04 below) the amount of
six months' of his Base Salary, provided the Executive shall be entitled to such
payments only if the Executive has not breached and does not breach the
provisions of Sections 6.01, 7.01, 8.01, 9.01 or 9.02 and the Executive has
entered into and not revoked a general release of claims reasonably satisfactory
to the Companies. Such amounts will be payable in equal monthly installments for
a period of twelve (12) months commencing on the first month anniversary of the
Date of Termination. In addition, promptly following an Unjustified Termination,
the Executive shall also be reimbursed all Reimbursable Expenses incurred by the
Executive prior to such Unjustified Termination.

      SECTION 5.03. JUSTIFIED TERMINATION. If the Employment Period shall be
terminated prior to the expiration of the third anniversary of the date hereof
(or the extension of the Employment Period pursuant to Section 5.01) (a) for
Cause, (b) as a result of the Executive's resignation or leaving of his
employment, other than for Good Reason, (c) as a result of the death or
Permanent Disability of the Executive, or (d) as a result of the Executive's
provision of written notice not to extend the Employment Period under Section
5.01 (collectively, a "JUSTIFIED TERMINATION"), the Executive shall be entitled
to receive solely (except as provided in Section 5.04 below) his Base Salary
through the Date of Termination and reimbursement of all Reimbursable Expenses
incurred by the Executive prior to such Justified Termination.

      SECTION 5.04. BENEFITS. Except as otherwise required by mandatory
provisions of law, all of the Executive's rights to fringe and other benefits
under this Agreement or otherwise, if any, accruing after the termination of the
Employment Period as a result of a Justified Termination will cease upon such
Justified Termination. Notwithstanding the foregoing, if such Justified
Termination is a result of a Permanent Disability or if the Employment Period is
terminated as a result of an Unjustified Termination, the Executive shall
continue to receive his major medical insurance coverage benefits from the
Company's plan in effect at the time of such termination for a period of twelve
(12) months after the Date of Termination.

      SECTION 5.05. NOTICE OF TERMINATION. Any termination by the Companies for
Permanent Disability or Cause or without Cause or by the Executive for Good
Reason shall be communicated by written Notice of Termination to the other party
hereto. For purposes of this Agreement, a "NOTICE OF TERMINATION" shall mean a
notice which shall indicate the specific termination provision in this Agreement
relied upon and shall set forth in reasonable detail the facts and circumstances
claimed to provide a basis for termination of employment under the provision
indicated.

<Page>
                                      -7-

      SECTION 5.06. DATE OF TERMINATION. "DATE OF TERMINATION" shall mean (a) if
the Employment Period is terminated as a result of a Permanent Disability, five
(5) days after a Notice of Termination is given, (b) if the Employment Period is
terminated for Good Reason, the date specified in the Notice of Termination, and
(c) if the Employment Period is terminated for any other reason (including for
Cause), the date designated by the Companies in the Notice of Termination.

                                    ARTICLE 6

                            CONFIDENTIAL INFORMATION

      SECTION 6.01. NONDISCLOSURE AND NONUSE OF CONFIDENTIAL INFORMATION. The
Executive will not disclose or use at any time during or after the Employment
Period any Confidential Information of which the Executive is or becomes aware,
whether or not such information is developed by him, except to the extent that
such disclosure or use is directly related to and required by the Executive's
performance of duties assigned to the Executive pursuant to this Agreement.
Under all circumstances and at all times, the Executive will take all
appropriate steps to safeguard Confidential Information in his possession and to
protect it against disclosure, misuse, espionage, loss and theft.

                                    ARTICLE 7

                              INTELLECTUAL PROPERTY

      SECTION 7.01. OWNERSHIP OF INTELLECTUAL PROPERTY. In the event that the
Executive as part of his activities on behalf of the Companies generates,
authors or contributes to any invention, design, new development, device,
product, method of process (whether or not patentable or reduced to practice or
comprising Confidential Information), any copyrightable work (whether or not
comprising Confidential Information) or any other form of Confidential
Information relating directly or indirectly to the business of the Companies as
now or hereinafter conducted (collectively, "INTELLECTUAL PROPERTY"), the
Executive acknowledges that such Intellectual Property is the sole and exclusive
property of the Companies and hereby assigns all right title and interest in and
to such Intellectual Property to the Companies. Any copyrightable work prepared
in whole or in part by the Executive during the Employment Period will be deemed
"a work made for hire" under Section 201(b) of the Copyright Act of 1976, as
amended, and the Companies will own all of the rights comprised in the copyright
therein. The Executive will promptly and fully disclose all Intellectual
Property and will cooperate with the Companies to protect the Companies'
interests in and rights to such Intellectual Property (including providing
reasonable assistance in securing patent protection and copyright registrations
and executing all documents as reasonably requested by the Companies, whether
such requests occur prior to or after termination of Executive's employment
hereunder).

<Page>
                                      -8-

                                    ARTICLE 8

              DELIVERY OF MATERLALS UPON TERMINATION OF EMPLOYMENT

      SECTION 8.01. DELIVERY OF MATERIALS UPON TERMINATION OF EMPLOYMENT. As
requested by the Companies, from time to time and upon the termination of the
Executive's employment with the Companies for any reason, the Executive will
promptly deliver to the Companies all copies and embodiments, in whatever form
or medium, of all Confidential Information or Intellectual Property in the
Executive's possession or within his control (including written records, notes,
photographs, manuals, notebooks, documentation, program listings, flow charts,
magnetic media, disks, diskettes, tapes and all other materials containing any
Confidential Information or Intellectual Property) irrespective of the location
or form of such material and, if requested by the Companies, will provide the
Companies with written confirmation that all such materials have been delivered
to the Companies.

                                    ARTICLE 9

                       NONCOMPETITION AND NONSOLICITATION

      SECTION 9.01. NONCOMPETITION. The Executive acknowledges that during his
employment with the Companies, he will become familiar with trade secrets and
other Confidential Information concerning the Companies, their Subsidiaries and
their respective predecessors, and that his services will be of special, unique
and extraordinary value to the Companies. In addition, the Executive hereby
agrees that at any time during the Employment Period, and for a period ending
two (2) years after the Date of Termination (if such termination is for Cause or
as a result of the Executive's resignation or leaving employment not for Good
Reason) (the "NONCOMPETITION PERIOD"), he will not directly or indirectly own,
manage, control, participate in, consult with, render services for or in any
manner engage in any business competing with the businesses of the Companies or
their Subsidiaries as such businesses exist or are in process or being planned
as of the Date of Termination, within any geographical area in which the
Companies or their Subsidiaries engage or plan to engage in such businesses.
Notwithstanding the foregoing, the Noncompetition Period shall be twelve (12)
months following the Date of Termination if such termination is by the Companies
without Cause, by the Executive for Good Reason or due to the Executive giving
written notice pursuant to Section 5.01 of his intention not to extend the
Employment Period; PROVIDED HOWEVER, that in such circumstances, the
Noncompetition Period may be extended up to a period of eighteen (18) months
following the Date of Termination by the Company if it elects in writing to pay
the Executive his Base Salary for the additional six (6) month period, such
amount to be payable in monthly installments over the additional six (6) month
period. It shall not be considered a violation of this Section 9.01 for the
Executive (i) to be a passive owner of not more than 2% of the outstanding stock
of any class of a corporation which is publicly traded, so

<Page>
                                      -9-

long as the Executive has no active participation in the business of such
corporation, or (ii) to serve as a nonemployee director of Fairfax Financial
Holdings or its subsidiary Odyssey Reinsurance.

      SECTION 9.02. NONSOLICITATION. The Executive hereby agrees that (a) during
the Employment Period and for a period of two (2) years after the Date of
Termination (the "Nonsolicitation Period") the Executive will not, directly or
indirectly through another entity, induce or attempt to induce any employee of
the Companies or their Subsidiaries to leave the employ of the Companies or
their Subsidiaries, or in any way interfere with the relationship between the
Companies or their Subsidiaries and any employee thereof or otherwise employ or
receive the services of any individual who was an employee of the Companies or
their Subsidiaries at any time during such Nonsolicitation Period or within the
six-month period prior thereto and (b) during the Nonsolicitation Period, the
Executive will not induce or attempt to induce any customer, supplier, client,
insured, reinsured, reinsurer, broker, licensee or other business relation of
the Companies or their Subsidiaries to cease doing business with the Companies
or their Subsidiaries.

      SECTION 9.03. ENFORCEMENT. If, at the enforcement of Sections 9.01 or
9.02, a court holds that the duration, scope or area restrictions stated herein
are unreasonable under circumstances then existing, the parties agree that the
maximum duration, scope or area reasonable under such circumstances will be
substituted for the stated duration, scope or area and that the court will be
permitted to revise the restrictions contained in this Section 9 to cover the
maximum duration, scope and area permitted by law.

                                   ARTICLE 10

                                EQUITABLE RELIEF

      SECTION 10.01. EQUITABLE RELIEF. The Executive acknowledges that (a) the
covenants contained herein are reasonable, (b) the Executive's services are
unique, and (c) a breach or threatened breach by him of any of his covenants and
agreements with the Companies contained in Sections 6.01, 7.01, 8.01, 9.01 or
9.02 could cause irreparable harm to the Companies for which they would have no
adequate remedy at law. Accordingly, and in addition to any remedies which the
Companies may have at law, in the event of an actual or threatened breach by the
Executive of his covenants and agreements contained in Sections 6.01, 7.01,
8.01, 9.01 or 9.02, the Companies shall have the absolute right to apply to any
court of competent jurisdiction for such injunctive or other equitable relief as
such court may deem necessary or appropriate in the circumstances.

<Page>
                                      -10-

                                   ARTICLE 11

                            EXECUTIVE REPRESENTATIONS

      SECTION 11.01. EXECUTIVE REPRESENTATIONS. The Executive hereby represents
and warrants to the Companies that (a) the execution, delivery and performance
of this Agreement by the Executive does not and will not conflict with, breach,
violate or cause a default under any contract, agreement, instrument, order,
judgment or decree to which the Executive is a party or by which he is bound,
(b) the Executive is not a party to or bound by any employment agreement,
noncompetition agreement or confidentiality agreement with any other Person and
(c) upon the execution and delivery of this Agreement by the Companies, this
Agreement will be the valid and binding obligation of the Executive, enforceable
in accordance with its terms.

                                   ARTICLE 12

                                  MISCELLANEOUS

      SECTION 12.01. REMEDIES. The Companies will have all rights and remedies
set forth in this Agreement, all rights and remedies which the Companies have
been granted at any time under any other agreement or contact and all of the
rights which the Companies have under any law. The Companies will be entitled to
enforce such rights specifically, without posting a bond or other security, to
recover damages by reason of any breach of any provision of this Agreement and
to exercise all other rights granted by law. There are currently no disciplinary
or grievance procedures in place, there is no collective agreement in place, and
there is no probationary period.

      SECTION 12.02. CONSENT TO AMENDMENTS. The provisions of this Agreement may
be amended or waived only by a written agreement executed and delivered by the
Companies and the Executive. No other course of dealing between the parties to
this Agreement or any delay in exercising any rights hereunder will operate as a
waiver of any rights of any such parties.

      SECTION 12.03. SUCCESSORS AND ASSIGNS. All covenants and agreements
contained in this Agreement by or on behalf of any of the parties hereto will
bind and inure to the benefit of the respective successors and assigns of the
parties hereto whether so expressed or not, PROVIDED that the Executive may not
assign his rights or delegate his obligations under this Agreement without the
written consent of the Companies.

      SECTION 12.04. SEVERABILITY. Whenever possible, each provision of this
Agreement will be interpreted in such manner as to be effective and valid under
applicable law, but if any provision of this Agreement is held to be prohibited
by or invalid under applicable law, such provision will be ineffective only to
the extent of such prohibition or invalidity, without invalidating the remainder
of this Agreement.

<Page>
                                      -11-

      SECTION 12.05. COUNTERPARTS. This Agreement may be executed simultaneously
in two or more counterparts, any one of which need not contain the signatures of
more than one party, but all of which counterparts taken together will
constitute one and the same agreement.

      SECTION 12.06. DESCRIPTIVE HEADINGS. The descriptive headings of this
Agreement are inserted for convenience only and do not constitute a part of this
Agreement.

      SECTION 12.07. NOTICES. All notices, demands or other communications to be
given or delivered under or by reason of the provisions of this Agreement will
be in writing and will be deemed to have been given when delivered personally to
the recipient, two (2) business days after the date when sent to the recipient
by reputable express courier service (charges prepaid) or four (4) business days
after the date when mailed to the recipient by certified or registered mail,
return receipt requested and postage prepaid. Such notices, demands and other
communications will be sent to the Executive and to the Companies at the
addresses set forth below.

      If to the Executive:    To the last address delivered to
                              the Companies by the Executive in the manner set
                              forth herein.

      If to Parent:           Arch Capital Group Ltd,
                              Executive Offices
                              20 Horseneck Lane
                              Greenwich, CT  06830

                              Attn:  General Counsel

      If to the Company:      Arch Reinsurance Ltd.
                              Richmond House
                              Par-la-Ville Road
                              Hamilton HM 11
                              Bermuda

                              Attn:  General Counsel

      Copies (which shall not constitute notice) of notices to Parent and the
      Company shall also be sent to:

<Page>
                                      -12-

                              Cahill Gordon & Reindel
                              80 Pine Street
                              New York, NY  10005

                              Attn:  Immanuel Kohn, Esq.

or to such other address or to the attention of such other person as the
recipient party has specified by prior written notice to the sending party.

      SECTION 12.08. WITHHOLDING. The Companies may withhold from any amounts
payable under this Agreement such federal, state, local or foreign taxes as
shall be required to be withheld pursuant to any applicable law or regulation.

      SECTION 12.09. NO THIRD PARTY BENEFICIARY. This Agreement will not confer
any rights or remedies upon any person other than the Companies, the Executive
and their respective heirs, executors, successors and assigns.

      SECTION 12.10. ENTIRE AGREEMENT. This Agreement (including the documents
referred to herein) constitutes the entire agreement among the parties and
supersedes any prior understandings, agreements or representations by or among
the parties, written or oral, that may have related in any way to the subject
matter hereof. This Agreement shall serve as a written statement of employment
for purposes of Section 6 of the Bermuda Employment Act 2000.

      SECTION 12.11. CONSTRUCTION. The language used in this Agreement will be
deemed to be the language chosen by the parties to express their mutual intent,
and no rule of strict construction will be applied against any party. Any
reference to any federal, state, local or foreign statute or law will be deemed
also to refer to all rules and regulations promulgated thereunder, unless the
context requires otherwise. The use of the word "INCLUDING" in this Agreement
means "including without limitation" and is intended by the parties to be by way
of example rather than limitation.

      SECTION 12.12. SURVIVAL. Sections 6.01, 7.01, 8.01 and Articles 9 and 12
will survive and continue in full force in accordance with their terms
notwithstanding any termination of the Employment Period.

      SECTION 12.13. GOVERNING LAW. ALL QUESTIONS CONCERNING THE CONSTRUCTION,
VALIDITY AND INTERPRETATION OF THIS AGREEMENT WILL BE GOVERNED BY THE INTERNAL
LAW OF BERMUDA, WITHOUT REGARD TO PRINCIPLES OF CONFLICT OF LAWS.

<Page>
                                      -13-

      IN WITNESS WHEREOF, the parties hereto have executed this Agreement as of
the date and year first above written.

                                    ARCH CAPITAL GROUP LTD.

                                    By: /s/ Louis T. Petrillo
                                       ------------------------------------
                                    Printed Name: Louis T. Petrillo
                                                 --------------------------
                                    Title: SVP, General Counsel & Secretary
                                          ---------------------------------

                                    ARCH REINSURANCE LTD.

                                    By: /s/ Graham B.R. Collis
                                       ------------------------------------
                                    Printed Name: Graham B.R. Collis
                                                 --------------------------
                                    Title: Director
                                          ---------------------------------

                                    /s/ Paul B. Ingrey
                                    ---------------------------------------
                                    Paul B. Ingrey

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