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                                                                   Exhibit 10.11

                             ARCH CAPITAL GROUP LTD.

                           RESTRICTED SHARE AGREEMENT

      THIS AGREEMENT, dated as of October 23, 2001, between Arch Capital Group
Ltd. (the "Company"), a Bermuda company, and Marc Grandisson (the "Employee").

      WHEREAS, the Employee has been granted the following award in connection
with his retention as an employee and as compensation for services to be
rendered; and the following terms reflect the Company's Long Term Incentive Plan
For New Employees (as amended, the "Plan");

      NOW, THEREFORE, in consideration of the premises and mutual covenants
contained herein, the parties hereto agree as follows.

      1. AWARD OF SHARES. Pursuant to the provisions of the Plan, the terms of
which are incorporated herein by reference, the Employee is hereby awarded
12,500 Restricted Shares (the "Award"), subject to the terms and conditions
herein set forth. Capitalized terms used herein and not defined shall have the
meanings set forth in the Plan. In the event of any conflict between this
Agreement and the Plan, the Plan shall control.

      2. TERMS AND CONDITIONS. It is understood and agreed that the Award of
Restricted Shares evidenced hereby is subject to the following terms and
conditions:

      (a) VESTING OF AWARD. Subject to Section 2(b) below and the other terms
and conditions of this Agreement, this Award shall become vested on the fifth
anniversary of the date hereof. Unless otherwise provided by the Company, all
dividends and other amounts receivable in connection with any adjustments to the
Shares under Section 4(c) of the Plan shall be subject to the vesting schedule
in this Section 2(a). Notwithstanding the foregoing, if (i) a Change in Control
occurs and (ii) within two years following such Change in Control, the
employment of the Employee is terminated by the Company not for Cause or
Permanent Disability (as defined in the Employment Agreement between the
Employee, the Company and Arch Reinsurance Ltd. dated as of October __, 2001
(the "Employment Agreement")) or the Employee terminates his employment with the
Company for Good Reason (as defined in the Employment Agreement), then the
Restricted Shares shall become immediately vested in full upon such termination
of employment.

      For purposes of this Agreement, a "Change in Control" shall be deemed to
occur if any "person" (within the meaning of the Securities Exchange Act of
1934, as amended (the "Exchange Act")), other than a Permitted Person, is or
becomes the "beneficial owner" (as defined in Rule 13d-3 under the Exchange
Act), directly or indirectly, of Voting Securities representing more than 50% of
the total voting power of all then outstanding Voting Securities.

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                                      -2-

      "Permitted Persons" means (A) the Company; (B) any Related Party; (C)
Hellman & Friedman or any of its subsidiaries or investment funds managed or
controlled by Hellman & Friedman; (D) Warburg Pincus or any of its subsidiaries
or any investment funds managed or controlled by Warburg Pincus or any of its
subsidiaries; or (E) any group (as defined in Rule 13b-3 under the Exchange Act)
comprised of any or all of the foregoing.

      "Related Party" means (A) a majority-owned subsidiary of the Company; (B)
a trustee or other fiduciary holding securities under an employee benefit plan
of the Company or any majority-owned subsidiary of the Company; or (C) any
entity, 50% or more of the voting power of which is owned directly or indirectly
by the stockholders of the Company in substantially the same proportion as their
ownership of Voting Securities immediately prior to the transaction.

      "Voting Security" means any security of the Company which carries the
right to vote generally in the election of directors.

      (b) TERMINATION OF SERVICE; FORFEITURE OF UNVESTED SHARES. Except as
otherwise set forth in Section 2(a) above, in the event the Employee ceases to
be an employee of the Company for any reason (other than due to his death or
Permanent Disability (as defined in the Employment Agreement)) prior to the date
the Award vests, the Award shall be forfeited by the Employee and become the
property of the Company. For purposes of this Agreement, service with any of the
Company's wholly owned subsidiaries shall be considered to be service with the
Company. If the Employee ceases to be an employee of the Company due to his
death or Permanent Disability on or before the first anniversary of the date
hereof, one-fifth of the Award will vest at the time of such termination. If the
Employee ceases to be an employee of the Company due to his death or Permanent
Disability after the first anniversary of the date hereof but on or before the
second anniversary of the date hereof, two-fifths of the Award will vest at the
time of such termination. If the Employee ceases to be an employee of the
Company due to his death or Permanent Disability after the second anniversary of
the date hereof but on or before the third anniversary of the date hereof,
three-fifths of the Award will vest at the time of such termination. If the
Employee ceases to be an employee of the Company due to his death or Permanent
Disability after the third anniversary of the date hereof but on or before the
fourth anniversary of the date hereof, four-fifths of the Award will vest at the
time of such termination. If the Employee ceases to be an employee of the
Company due to his death or Permanent Disability after the fourth anniversary of
the date hereof, the Award will vest in full at the time of such termination.

      (c) CERTIFICATES. Each certificate issued in respect of Restricted Shares
awarded hereunder shall be deposited with the Company, or its designee, together
with, if requested by the Company, a stock power executed in blank by the
Employee, and shall bear a legend disclosing the restrictions on transferability
imposed on such Restricted Shares by this Agreement (the "Restrictive Legend").
Upon the vesting of Restricted Shares pursuant to Section 2(a) hereof and the
satisfaction of any withholding tax liability

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                                      -3-

pursuant to Section 5 hereof, the certificates evidencing such vested Shares,
not bearing the Restrictive Legend, shall be delivered to the Employee.

      (d) RIGHTS OF A STOCKHOLDER. Prior to the time a Restricted Share is fully
vested hereunder, the Employee shall have no right to transfer, pledge,
hypothecate or otherwise encumber such Restricted Share. During such period, the
Employee shall have all other rights of a stockholder, including, but not
limited to, the right to vote and to receive dividends (subject to Section 2(a)
hereof) at the time paid on such Restricted Shares.

      (e) NO RIGHT TO CONTINUED EMPLOYMENT. This Award shall not confer upon the
Employee any right with respect to continuance of employment by the Company nor
shall this Award interfere with the right of the Company to terminate the
Employee's employment at any time.

      3. TRANSFER OF SHARES. The Shares delivered hereunder, or any interest
therein, may be sold, assigned, pledged, hypothecated, encumbered, or
transferred or disposed of in any other manner, in whole or in part, only in
compliance with the terms, conditions and restrictions as set forth in the
governing instruments of the Company, applicable United States federal and state
securities laws or any other applicable laws or regulations and the terms and
conditions hereof.

      4. EXPENSES OF ISSUANCE OF SHARES. The issuance of stock certificates
hereunder shall be without charge to the Employee. The Company shall pay, and
indemnify the Employee from and against any issuance, stamp or documentary taxes
(other than transfer taxes) or charges imposed by any governmental body, agency
or official (other than income taxes) or by reason of the issuance of Shares.

      5. WITHHOLDING. No later than the date of vesting of the Award granted
hereunder, the Employee shall pay to the Company or make arrangements
satisfactory to the Committee regarding payment of any federal, state or local
taxes of any kind required by law to be withheld upon the vesting of such Award
and the Company shall, to the extent permitted or required by law, have the
right to deduct from any payment of any kind otherwise due to the Employee,
federal, state and local taxes of any kind required by law to be withheld upon
the vesting of such Award.

      6. REFERENCES. References herein to rights and obligations of the Employee
shall apply, where appropriate, to the Employee's legal representative or estate
without regard to whether specific reference to such legal representative or
estate is contained in a particular provision of this Agreement.

      7. NOTICES. Any notice required or permitted to be given under this
Agreement shall be in writing and shall be deemed to have been given when
delivered personally or by courier, or sent by certified or registered mail,
postage prepaid, return receipt requested, duly addressed to the party concerned
at the address indicated below or to such changed address as such party may
subsequently by similar process give notice of:

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                                      -4-

       If to the Company:

       Arch Capital Group Ltd.
       EXECUTIVE OFFICES:
       20 Horseneck Lane
       Greenwich, CT 06830
       Attn.: Secretary

       If to the Employee:

      To the last address delivered to the Company by the Executive in the
      manner set forth herein.

      8. GOVERNING LAW. This Agreement shall be governed by and construed in
accordance with the laws of Bermuda, without giving effect to principles of
conflict of laws.

      9. ENTIRE AGREEMENT. This Agreement and the Plan constitutes the entire
agreement among the parties relating to the subject matter hereof, and any
previous agreement or understanding among the parties with respect thereto is
superseded by this Agreement and the Plan.

      10. COUNTERPARTS. This Agreement may be executed in two counterparts, each
of which shall constitute one and the same instrument.

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                                      -5-

      IN WITNESS WHEREOF, the undersigned have executed this Agreement as of the
date first above written.

                                        ARCH CAPITAL GROUP LTD.

                                        By: /s/ Louis T. Petrillo
                                            ----------------------------------

                                        /s/ Marc Grandisson
                                        ---------------------------------------
                                        Marc Grandisson<Page>
                                                                   Exhibit 10.12

                             ARCH CAPITAL GROUP LTD.

                           RESTRICTED SHARE AGREEMENT

      THIS AGREEMENT, dated as of January 30, 2001, between Arch Capital Group
Ltd. (the "Company"), a Bermuda company, and Louis T. Petrillo (the "Employee").

      WHEREAS, the Employee has been granted the following award in connection
with his retention as an employee and as compensation for services to be
rendered; and the following terms reflect the Company's 1995 Long Term Incentive
and Share Award Plan (as amended, the "Plan");

      NOW, THEREFORE, in consideration of the premises and mutual covenants
contained herein, the parties hereto agree as follows.

      1. AWARD OF SHARES. Pursuant to the provisions of the Plan, the terms of
which are incorporated herein by reference, the Employee is hereby awarded 5,000
Restricted Shares (the "Award"), subject to the terms and conditions herein set
forth. Capitalized terms used herein and not defined shall have the meanings set
forth in the Plan.

      2. TERMS AND CONDITIONS. It is understood and agreed that the Award of
Restricted Shares evidenced hereby is subject to the following terms and
conditions:

            (a) VESTING OF AWARD. Subject to the other terms and conditions of
      this Agreement, this Award shall become vested in accordance with the
      following schedule:

                                                The Following Number
                                                of Restricted Shares
                                                Shall Vest on
            On This Date                        Each Respective Date
            ------------                        ---------------------
              1/30/02                                  1,250
              1/30/03                                  1,250
              1/30/04                                  1,250
              1/30/05                                  1,250

      ; provided that all such shares shall immediately become vested (i) to the
      extent provided in Section 2(b) hereof and (ii) upon a Change in Control.

            "Change in Control" means any of the following occurring after the
      date hereof:

                  a. any person (within the meaning of the Securities Exchange
            Act of 1934, as amended (the "Exchange Act")), other than a
            Permitted Person or an Initial Investor, is or becomes the
            "beneficial owner" (as defined in Rule 13d-3 under the Exchange
            Act), directly or indirectly, of Voting Securities representing 35%
            or more of the total voting power of all the then outstanding Voting
            Securities; or

                  b. any Initial Investor is or becomes the "beneficial owner"
            (as defined in Rule 13d-3 under the Exchange Act), directly or
            indirectly, of Voting Securities representing 50% percent or more of
            the total voting power of all the then outstanding Voting
            Securities; or

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                  c. the individuals who, as of the date hereof, constitute the
            Board of Directors of the Company (the "Board") together with those
            who become directors subsequent to such date and whose
            recommendation, election or nomination for election to the Board was
            approved by a vote of at least a majority of the directors then
            still in office who either were directors as of such date or whose
            recommendation, election or nomination for election was previously
            so approved, cease for any reason to constitute a majority of the
            members of the Board; or

                  d. the consummation of a merger, consolidation,
            recapitalization, liquidation, sale or disposition by the Company of
            all or substantially all of the Company's assets, or reorganization
            of the Company, other than any such transaction which would (x)
            result in at least 60% of the total voting power represented by the
            voting securities of the surviving entity or, in the case of an
            asset sale, the successor entity, outstanding immediately after such
            transaction being beneficially owned, directly or indirectly, by the
            stockholders of the Company immediately preceding the transaction
            and (y) not otherwise be deemed a Change in Control under
            subparagraphs a, b, c or e of this Section 2(a); or

                  e. the Board adopts a resolution to the effect that, for
            purposes hereof, a Change in Control has occurred.

                        (i) "Initial Investors" means (A) The Trident
                        Partnership, L.P.; (B) Marsh & McLennan Risk Capital
                        Holdings, Ltd.; or (C) any majority-owned subsidiary or
                        parent (or equivalent in the case of a non-corporate
                        entity) of the foregoing.

                        (ii) "Permitted Persons" means (A) the Company; (B) any
                        Related Party; or (C) any group (as defined in Rule
                        13d-3 under the Exchange Act) comprised of any or all of
                        the foregoing.

                        (iii) "Related Party" means (A) a majority-owned
                        subsidiary of the Company; (B) a trustee or other
                        fiduciary holding securities under an employee benefit
                        plan of the Company or any majority-owned subsidiary of
                        the Company; or (C) a corporation owned directly or
                        indirectly by the stockholders of the Company in
                        substantially the same proportion as their ownership of
                        Voting Securities.

                        (iv) "Voting Security" means any security of the Company
                        which carries the right to vote generally in the
                        election of directors.

            (b) TERMINATION OF SERVICE; FORFEITURE OF UNVESTED SHARES. In the
      event the Employee ceases to be an employee of the Company (i) due to
      retirement after attainment of age 65 or (ii) due to death or disability,
      as determined under the Company's long-term disability plan, the
      Restricted Shares subject to the Award, to the extent not already vested
      in full, shall become immediately and fully vested at the time of such
      termination of service. If the Employee ceases to be an employee of the
      Company for any other reason, the portion of the Award which is not then
      vested shall be forfeited by the Employee and become the property of the
      Company. For purposes of this Agreement, service with any of the Company's
      wholly owned subsidiaries shall be considered to be service with the
      Company.

            (c) CERTIFICATES. Each certificate issued in respect of Restricted
      Shares awarded hereunder shall be deposited with the Company, or its
      designee, together with, if requested by the

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      Company, a stock power executed in blank by the Employee, and shall bear a
      legend disclosing the restrictions on transferability imposed on such
      Restricted Shares by this Agreement (the "Restrictive Legend"). Upon the
      vesting of Restricted Shares pursuant to Section 2(a) or 2(b) hereof and
      the satisfaction of any withholding tax liability pursuant to Section 5
      hereof, the certificates evidencing such vested Shares, not bearing the
      Restrictive Legend, shall be delivered to the Employee.

            (d) RIGHTS OF A STOCKHOLDER. Prior to the time a Restricted Share is
      fully vested hereunder, the Employee shall have no right to transfer,
      pledge, hypothecate or otherwise encumber such Restricted Share. During
      such period, the Employee shall have all other rights of a stockholder,
      including, but not limited to, the right to vote and to receive dividends
      at the time paid on such Restricted Shares.

            (e) NO RIGHT TO CONTINUED EMPLOYMENT. This Award shall not confer
      upon the Employee any right with respect to continuance of employment by
      the Company nor shall this Award interfere with the right of the Company
      to terminate the Employee's employment at any time.

      3. TRANSFER OF SHARES. The Shares delivered hereunder, or any interest
therein, may be sold, assigned, pledged, hypothecated, encumbered, or
transferred or disposed of in any other manner, in whole or in part, only in
compliance with the terms, conditions and restrictions as set forth in the
governing instruments of the Company, applicable United States federal and state
securities laws or any other applicable laws or regulations and the terms and
conditions hereof. Each certificate for Shares delivered hereunder, unless at
the time of issuance such Shares are registered under the Securities Act of
1933, as amended, shall bear the following legend or such other legend as the
Company deems appropriate:

      "The securities evidenced hereby have not been registered under the
      Securities Act of 1933, as amended (the 'Act'), and may not be offered,
      sold or otherwise transferred except (i) in compliance with the provisions
      of any applicable state securities or 'Blue Sky' laws and (ii) (A)
      pursuant to an effective registration under the Act, (B) in compliance
      with Rule 144 under the Act, (C) inside the United States to a Qualified
      Institutional Buyer in compliance with Rule 144A under the Act, (D)
      outside the United States in compliance with Rule 904 of Regulation S
      under the Act or (E) inside the United States to an institutional
      'accredited investor' as defined in Rule 501(a)(1), (2), (3) or (7) under
      the Act in a transaction which, in the opinion of counsel reasonably
      satisfactory to the Company, qualifies as an exempt transaction under the
      Act and the rules and regulations promulgated thereunder."

Any certificate issued at any time in exchange or substitution for any
certificate bearing such legend or such other legend deemed appropriate by the
Company shall also bear such legend unless, in the opinion of counsel for the
Company, the securities represented thereby need no longer be subject to the
restriction contained herein. The provisions of this Section 3 shall be binding
upon all subsequent holders of certificates bearing the above legend.

      4. EXPENSES OF ISSUANCE OF SHARES. The issuance of stock certificates
hereunder shall be without charge to the Employee. The Company shall pay, and
indemnify the Employee from and against any issuance, stamp or documentary taxes
(other than transfer taxes) or charges imposed by any governmental body, agency
or official (other than income taxes) or by reason of the issuance of Shares.

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      5. WITHHOLDING. The Employee agrees to make appropriate arrangements with
the Company for satisfaction of any applicable tax withholding requirements, or
similar requirements, arising out of this Agreement.

      6. REFERENCES. References herein to rights and obligations of the Employee
shall apply, where appropriate, to the Employee's legal representative or estate
without regard to whether specific reference to such legal representative or
estate is contained in a particular provision of this Agreement.

      7. SETTLEMENT OF DISPUTES. Any dispute between the parties arising from or
relating to the terms of this Agreement shall be resolved by arbitration held in
the State of Connecticut in accordance with the rules of the American
Arbitration Association. All costs associated with any arbitration, including
all legal expenses, for both parties shall be borne by the Company.

      8. NO MITIGATION. To the extent that the vesting of any portion of the
Award is accelerated upon a Change in Control or upon a termination of service
as provided herein, neither the Shares delivered hereunder nor any interest
therein, shall be reduced by any compensation received by the Employee in
connection with any other employment.

      9. NOTICES. Any notice required or permitted to be given under this
Agreement shall be in writing and shall be deemed to have been given when
delivered personally or by courier, or sent by certified or registered mail,
postage prepaid, return receipt requested, duly addressed to the party concerned
at the address indicated below or to such changed address as such party may
subsequently by similar process give notice of:

      If to the Company:

            Arch Capital Group Ltd.
            EXECUTIVE OFFICES:
            20 Horseneck Lane
            Greenwich, CT 06830
            Attn.: Secretary

      If to the Employee:

            Louis T. Petrillo
            124 W. 60th Street, Apt. 43F
            New York, N.Y. 10023

      10. GOVERNING LAW. This Agreement shall be governed by and construed in
accordance with the laws of the State of New York, without giving effect to
principles of conflict of laws.

      11. ENTIRE AGREEMENT. This Agreement constitutes the entire agreement
among the parties relating to the subject matter hereof, and any previous
agreement or understanding among the parties with respect thereto is superseded
by this Agreement.

      12. COUNTERPARTS. This Agreement may be executed in two counterparts, each
of which shall constitute one and the same instrument.

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      IN WITNESS WHEREOF, the undersigned have executed this Agreement as of the
date first above written.

                                       ARCH CAPITAL GROUP LTD.

                                       By: /s/ Peter A. Appel
                                           ------------------------------------
                                           Peter A. Appel
                                           President and Chief Executive Officer

                                       /s/ Louis T. Petrillo
                                       ----------------------------------------
                                       Louis T. Petrillo

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