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                                                                    Exhibit 10.2

                             ARCH CAPITAL GROUP LTD.

                                    AGREEMENT

           THIS AGREEMENT, dated November 12, 2002, between Arch Capital Group
Ltd. (the "COMPANY"), a Bermuda company, and Robert Clements (the "EXECUTIVE");

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

         1. To the extent that (a) the Executive seeks capital gains treatment
for U.S. federal income tax purposes (or any corresponding provisions of state
or local tax law) on any gains on the sales (the "REPURCHASES") to the Company
of common shares of the Company pursuant to the Share Repurchase Agreement,
dated November 6, 2002, and (b) the proceeds of such Repurchases are
characterized as ordinary dividend income for U.S. federal income tax purposes
(or any corresponding provisions of state or local tax law), then the Company
shall indemnify and hold the Executive harmless, on an after-tax basis, for any
such ordinary income taxes payable in excess of the capital gains taxes (long-
or short-term, depending on the applicable holding periods) relating to such
Repurchases.

         2. The Executive agrees to (a) file on a timely basis the income tax
returns relating to such Repurchases and (b) provide the Company with any
information reasonably requested by the Company relating to the reporting
position to be taken by the Executive for such Repurchases.

           3. This agreement shall be governed by and construed in accordance
with the laws of Connecticut, without giving effect to principles of conflict of
laws, and may be executed in two counterparts, each of which shall constitute
one and the same instrument.

           IN WITNESS WHEREOF, the undersigned have executed this agreement on
the date first above written.

                                      ARCH CAPITAL GROUP LTD.


                                      By: /s/ John D. Vollaro
                                          --------------------------------------
                                         Name: John D. Vollaro
                                         Title: Executive Vice President & Chief
                                               Financial Officer


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