Document:

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                                                                    Exhibit 10.9

                             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 Paul B. Ingrey (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
422,407 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 third 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 23, 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-third 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-thirds 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, 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 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 re-

<Page>
                                      -3-

      ceive 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:

<Page>
                                      -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.

<Page>
                                      -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
                                            ------------------------------------
                                            Louis T. Petrillo
                                            Senior Vice President, General
                                              Counsel and Secretary

                                        /s/ Paul B. Ingrey
                                        ----------------------------------------
                                        Paul B. Ingrey<Page>
                                                                   Exhibit 10.10

                             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 Dwight R. Evans (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
50,000 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. 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 third 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 23, 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.

<Page>
                                      -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-third 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-thirds 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, 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 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 re-

<Page>
                                      -3-

      ceive 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:

      If to the Company:

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

<Page>
                                      -4-

      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.

<Page>
                                      -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/ Dwight R. Evans
                                        ---------------------------------------
                                        Dwight R. Evans

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