Exhibit 10.2

NON-CORE BUSINESS PAYMENT AGREEMENT

This Non-Core Business Payment Agreement (the “Agreement”) is entered into on this 4th day of August, 2003, between Arch Capital Group Ltd. (the “Company”) and Peter Appel (the “Executive”).

For good and valuable consideration, the receipt and sufficiency of which is hereby acknowledged, the Executive and the Company agree as follows:

1.             The Executive will be paid an amount equal to $1,500,000 if, and only if, the aggregate of the Realized Values of all of the Non-Core Assets equals or exceeds the aggregate of the Adjusted Closing Book Values of all of the Non-Core Assets, computed as of the Test Date.

2.             The Executive will also be paid an amount equal to 15% of the net excess, if any, of the Realized Value over the Adjusted Closing Book Value of all of the Non-Core Assets, computed as of the Test Date; provided, however that any amount payable under this paragraph 2 shall not exceed $1,500,000 (such that the aggregate amount payable under paragraphs 1 and 2 of this Agreement shall not exceed $3 million).

3.             The amount, if any, payable under this Agreement shall be paid within 30 days following the date all of the computations of excesses of Realized Values over Adjusted Closing Book Values of the Non-Core Assets are finally determined for purposes of computing the Adjustment Basket under the Subscription Agreement made as of October 24, 2001 between the Company and the Purchasers thereunder (the “Subscription Agreement”).

4.             All capitalized terms used herein but not defined shall have the meanings given to them in the Subscription Agreement; provided, however, that for all purposes under this Agreement and under the Subscription Agreement “Realized Value” shall not be reduced by the amount, if any, payable under this Agreement.

5.             The Company shall cause the Executive to be provided, through December 31, 2003, access to office equipment for his home office and secretarial support as reasonably necessary in connection with the Executive’s activities in assisting with the disposition of the Non-Core Assets.  The Company shall reimburse the Executive, or cause the Executive to be reimbursed, for the reasonable business expenses incurred by him in connection with the disposition of the Non-Core Assets which are consistent with the Company’s expense reimbursement policies in effect from time to time, including reasonably necessary travel and lodging expenses, subject to the Company’s requirements with respect to reporting and documentation of expenses.  Promptly after December 31, 2003 upon the request of the Company, the Executive shall return all of the Company’s and its subsidiaries’ property in the Executive’s possession, including, but not limited to, the Company’s and its subsidiaries’ office equipment, software and peripherals and originals or copies of books, records, or other information pertaining to the business of the Company and its subsidiaries.  Such return may be effected by the Executive’s making the property available at his home for retrieval by the Company.

6.             All amounts payable hereunder shall be reduced by amounts required to be withheld for income, employment, social security or other taxes.

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7.             This Agreement shall be governed by and construed in accordance with the laws of the State of New York, without reference to the principles of conflict of laws thereof.

8.             This Non-Core Business Payment Agreement and the Agreement between the Executive and the Company of even date herewith represent the complete agreement between the Executive and the Company concerning the subject matter in such agreements, and they supersede all prior agreements or understandings, written or oral.  This Agreement may not be amended or modified otherwise than by a written agreement executed by the parties hereto or their respective successors and legal representatives.

9.             Each of the paragraphs contained in this Agreement shall be enforceable independently of every other paragraph in this Agreement, and the invalidity or unenforceability of any paragraph shall not invalidate or render unenforceable any other paragraph contained in this Agreement.

10.           The Company will require any successor or assignee, whether direct or indirect, by purchase, merger, consolidation or otherwise, of all, or substantially all, of the business and/or assets of the Company to assume and agree to perform this Agreement in the same manner and to the same extent that the Company would be required to perform it if such succession or assignment had not taken place.

11.           This Agreement shall inure to the benefit of and be enforceable by the Executive’s personal and legal representatives, executors, administrators, heirs, distributees, devisees and legatees.  If the Executive dies while any amounts are still payable to him

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hereunder, all such amounts, unless otherwise provided herein, shall be paid in accordance with the terms of this Agreement to the Executive’s devisee, legatee, or other designee or, if there be no such designee, to the Executive’s estate.

The parties to this Agreement have executed this Agreement on the day and year first written above.

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