Exhibit 10.4

ARCH CAPITAL GROUP LTD. INCENTIVE COMPENSATION PLAN

SECTION 1.  Purpose.

Arch Capital Group Ltd., a Bermuda company (the “Company”), hereby establishes this Incentive Compensation Plan (as amended from time to time, the “Plan”) in order to provide the Company’s employees with an opportunity to earn annual bonus compensation as an incentive and reward for their efforts to achieve the financial and strategic objectives of the Company.

SECTION 2.  Definitions.

2.1                                 “After-Tax Profit (Loss)” has the meaning specified on Schedule I hereto.

2.2                                 “Aggregate Target Amount” has the meaning specified in Section 4.3(a) hereof.

2.3                                 “Award” means the amount of bonus compensation to which an Eligible Employee is entitled for each Plan Year as determined by the Committee pursuant to Section 4 and 5 of the Plan, which may be paid in cash, restricted common shares of the Company or stock options as provided in Section 5 of the Plan.

2.4                                 “Board” means the Board of Directors of the Company.

2.5                                 “Cash Flow” has the meaning specified on Schedule I hereto.

2.6                                 “CAT Business” means business classified by the Company as property catastrophe reinsurance.

2.7                                 “Cause” means, with respect to an Eligible Employee, (a) theft or embezzlement by the Eligible Employee with respect to the Company or its Subsidiaries; (b) malfeasance or negligence in the performance of the Eligible Employee’s duties; (c) the commission by the Eligible Employee of any felony or any crime involving moral turpitude; (d) willful or prolonged absence from work by the Eligible Employee (other than by reason of disability due to physical or mental illness); (e) failure, neglect or refusal by the Eligible Employee to adequately perform his or her duties and responsibilities as determined by the Committee; (f) continued and habitual use of alcohol by the Eligible Employee to an extent which materially impairs the Eligible Employee’s performance of his or her duties without the same being corrected within ten (10) days after being given written notice thereof; or (g) the Eligible Employee’s use of illegal drugs without the same being corrected within ten (10) days after being given written notice thereof.

2.8                                 “Code” means the Internal Revenue Code of 1986, as amended, including applicable regulations thereunder.

2.9                                 “Committee” means the Compensation Committee of the Board, or such other Board committee or subcommittee (or the entire Board) as may be designated by the Board to administer the Plan.

2.10                           “Company” has the meaning specified in Section 1 hereof or any successor.

2.11                           “Deficits” has the meaning specified in Section 4.3(d) hereof.

2.12                           “Development Period” has the meaning specified in Section 4.3(e) hereof.

2.13                           “Eligible Employee” means an employee of the Company or its Subsidiaries, including any director who is an employee, who is selected to participate in the Plan by the Committee.

2.14                           “Employer” means the Company, Arch Reinsurance Ltd., Arch Reinsurance Company, Arch Capital Group (U.S.) Inc., Arch Insurance Group Inc. and its Subsidiaries, Arch Capital Services Inc., and any other Subsidiary of the Company that becomes an Employer in accordance with Section 8.1 hereof.

2.15                           “Equity” has the meaning specified on Schedule I hereto.

2.16                           “Formula Approach” has the meaning specified in Section 4.1 hereof.

2.17                           “Formula Approach Pool” has the meaning specified in Section 4.3(a) hereof.

2.18                           “Hurdle ROE” has the meaning specified in Section 4.3(b) hereof.

2.19                           “Insurance Segment” means the business segment of the Company consisting of its core insurance Subsidiaries, including Arch Insurance Group Inc. and its Subsidiaries, and any other insurance Subsidiary of the Company that becomes an Employer in accordance with Section 8.1 hereof.

2.20                           “Investment Income” has the meaning specified on Schedule I hereto.

2.21                           “Maximum Carryforward Amount” has the meaning specified in Section 4.3(c) hereof.

2.22                           “Maximum Formula Approach Pool” has the meaning specified in Section 4.3(c) hereof

2.23                           “Operating Expenses” has the meaning specified on Schedule I hereto.

2.24                           “Permanent Disability” means, with respect to an Eligible Employee, those circumstances where the Eligible Employee is unable to continue to perform the usual customary duties of his or her assigned job 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 Company and approved by the Eligible Employee (which

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approval shall not be unreasonably withheld).  The determination of any such physician shall be final and conclusive for all purposes of this Plan.

2.25                           “Plan” has the meaning specified in Section 1 hereof.

2.26                           “Plan Year” means (i) with respect to the Target Bonus Approach, a calendar year and (ii) with respect to the Formula Approach, an underwriting (or policy) year commencing on January 1 and ending on December 31 during which an accounting shall be made for all Underwriting Profit (Loss) attributable to Policies having an inception or renewal date during such 12-month period.

2.27                           “Policies” means policies, binders, contracts or agreements of insurance or reinsurance.

2.28                           “Reinsurance Segment” means the business segment of the Company consisting of its core reinsurance Subsidiaries, including Arch Reinsurance Ltd. and Arch Reinsurance Company, and any other reinsurance Subsidiary of the Company that becomes an Employer in accordance with Section 8.1 hereof.

2.29                           “ROE” has the meaning specified on Schedule I hereto.

2.30                           “Senior Executives” has the meaning set forth in Section 4.1 hereof.

2.31                           “Subsidiary” means any corporation (other than the Company) in an unbroken chain of corporations beginning with the Company if each of the corporations (other than the last corporation in the unbroken chain) owns shares possessing 50% or more of the total combined voting power of all classes of stock in one of the other corporations in the chain.

2.32                           “Target Bonus Approach” has the meaning specified in Section 4.1 hereof.

2.33                           “Target Bonus Approach Pool” has the meaning specified in Section 4.2(a) hereof.

2.34                           “Target Bonus Opportunity” means, with respect to each Eligible Employee, a target bonus expressed as a percentage of his or her annual base salary, which is intended as an approximation of the bonus payment that would be paid if aggressive performance goals and other expectations are met by both the Eligible Employee and the business segment or unit he or she is employed by.  The Target Bonus Opportunity for each Eligible Employee shall be periodically established (i) by senior management of the applicable business segment or unit and (ii) by the Committee, in the case of certain Senior Executives designated by the Committee (subject to applicable employment agreements).

2.35                           “Underwriting Profit (Loss)” has the meaning specified on Schedule I hereto.

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SECTION 3.                            Administration.

The Plan shall be administered by the Committee.  The Committee shall have the authority, in its sole discretion, to administer the Plan and to exercise all of the powers and authorities either specifically granted to it under the Plan or necessary or advisable in the administration of the Plan, including, without limitation, the authority to (i) establish performance goals for the awarding of Awards for each Plan Year; (ii) determine the Eligible Employees to whom Awards are to be made for each Plan Year; (iii) determine whether performance goals for each Plan Year have been achieved; (iv) authorize payment of Awards under the Plan; (v) adopt, alter and repeal such administrative rules, guidelines and practices governing the Plan and make all other determinations and judgments relating to the Plan as it shall deem advisable; and (vi) interpret the terms and provisions of the Plan; provided that neither the Committee nor the Board shall have any discretion to reduce any previously determined Award.  All determinations made by the Committee with respect to the Plan and Awards thereunder shall be final and binding on all persons, including the Company and all Eligible Employees.

SECTION 4.                            Determination of Awards.

4.1                                 Performance Measures.  The Plan combines two sets of performance measures:  (i) a qualitative judgment about progress and performance each Plan Year based on a number of factors, including the management plan for such Plan Year and non-prescribed measures (the “Target Bonus Approach”), as set forth in Section 4.2 hereof; and (ii) a quantitative, formula-based measure (the “Formula Approach”), as set forth in Section 4.3 hereof.  The Target Bonus Approach shall apply to certain senior executives (the “Senior Executives”) of each of the insurance and reinsurance Subsidiaries of the Company designated by the Committee from time to time.  The Formula Approach shall apply to those Eligible Employees designated by the Senior Executives.  All Eligible Employees of Arch Capital Services Inc. and any non-designated Eligible Employees shall be subject to the Target Bonus Approach.  Awards under the Target Bonus Approach and the Formula Approach shall be determined as set forth in Section 4.2 and Section 4.3, respectively, and shall be payable as set forth in Section 5 hereof.

4.2                                 Target Bonus Approach.

(a)                                  Target Bonus Approach Pool.  Under the Target Bonus Approach, a separate bonus pool shall be established for the Company, the Insurance Segment, the Reinsurance Segment and Arch Capital Services Inc. for each Plan Year (each, a “Target Bonus Approach Pool”).  The Target Bonus Approach Pool for each segment for any given Plan Year shall initially equal the sum of the individual Target Bonus Opportunities for each Eligible Employee included in such segment, which amount shall be adjusted upward or downward to reflect the segment’s actual performance as recommended by senior management of the applicable business segment or unit but determined by the Committee.  Performance shall be judged against the achievement of the strategic and financial objectives

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contained in the applicable management plan submitted to the Board for the Plan Year, peer group performance and other measures deemed applicable by the Committee.

(b)                                 Individual Participation.  At the individual level, actual performance bonuses for each Eligible Employee shall reflect both individual and segment performance.  An Eligible Employee’s participation in the applicable Target Bonus Approach Pool shall be initially based on his or her Target Bonus Opportunity, which participation shall be adjusted based on his or her performance.  Any such adjustments shall be made in a zero sum manner and not affect the overall size of the Target Bonus Approach Pool.  All performance assessments shall include both objective and subjective elements, and the general performance weighting guidelines between segment and individual performance to be applied to an Eligible Employee’s Target Bonus Opportunity shall be determined by senior management of the applicable business segment or unit.

4.3                                 Formula Approach.

(a)                                  Formula Approach Pool.  Under the Formula Approach, a separate bonus pool shall be established for the Insurance Segment and the Reinsurance Segment for each Plan Year (each, a “Formula Approach Pool”).  Unless otherwise determined by the Committee, any Underwriting Profit (Loss) generated from business initially underwritten by the Insurance Segment and re-underwritten by the Reinsurance Segment shall be applied solely to the Insurance Segment’s Formula Approach Pool.  The Formula Approach Pool for each of the Insurance Segment and the Reinsurance Segment for any given Plan Year shall initially equal the sum of the individual Target Bonus Opportunities for each Eligible Employee included in such segment (each, an “Aggregate Target Amount”).  The actual Formula Approach Pool would be a percentage of the Aggregate Target Amount based upon the ROE achieved for such Plan Year.  Schedule II sets forth the size of the Formula Approach Pool based on various levels of ROE, which schedule shall be reviewed and may be adjusted by the Committee for each Plan Year.

(b)                                 Hurdle ROE.  With respect to the Insurance Segment and the Reinsurance Segment, no Awards shall be payable in a given Plan Year unless a minimum ROE of 8%, without taking into account any amounts carried forward pursuant to Section 5.3(c) hereof (the “Hurdle ROE”), is achieved by such segment for such Plan Year.

(c)                                  Maximum Formula Approach Pool; Carryforwards.  For any given Plan Year, the maximum Formula Approach Pool for each of the Insurance Segment and the Reinsurance Segment shall equal 200% of the applicable Aggregate Target Amount (each, a “Maximum Formula Approach Pool”).  Amounts in excess of each Maximum Formula Approach Pool up to an additional 200% of such Maximum Formula Approach Pool (the “Maximum Carryforward Amount”) shall be carried forward and made available in Plan Years where the applicable Maximum Formula Approach Pool is not met,

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provided that the amount which may be carried forward to any subsequent Plan Year shall not exceed 25% of the Maximum Carryforward Amount.

(d)                                 Deficits.  After-Tax Losses (and not After-Tax Profit that is below the Hurdle ROE) for a given Plan Year (“Deficits”) shall offset available After-Tax Profit in subsequent Plan Years until all Deficits are eliminated.

(e)                                  Development Period.  For each Plan Year, the Formula Approach Bonus Pool for each of the Insurance Segment and the Reinsurance Segment shall be calculated annually for 10 years (a “Development Period”).  The first calculation shall be made within three months following the end of the initial 12-month calendar year period included in each Plan Year, and the final calculation shall be made within three months following the end of the tenth year following the commencement of such Plan Year, with losses and loss adjustment expenses (if any) projected to ultimate and discounted to present value basis at such time.

(f)                                    CAT Business.  The results of CAT Business shall be calculated over five-year periods based on actual catastrophe experience (terrorism included).  Accordingly, at the end of (i) the fifth Plan Year and (ii) each five-year period thereafter, Underwriting Profit (Loss) and Cash Flow shall be initially determined for CAT Business for such five-year period, and then such Underwriting Profit (Loss) and Cash Flow shall be allocated to each Plan Year included in the five-year period based on net premiums written attributable to CAT Business Policies having an inception or renewal date within such Plan Year.  Following such initial calculation, the results of CAT Business shall be part of the annual recalculations of Underwriting Profit (Loss) and Cash Flow for the remainder of the respective Development Period relating to each Plan Year.

(g)                                 Individual Participation.  Individual participation in the applicable Formula Approach Pool shall be initially determined based on the relative Target Bonus Opportunity of each of the designated Eligible Employees and shall be subject to adjustment each Plan Year by senior management of the applicable business segment or unit based on criteria it deems appropriate, provided that any such adjustments shall be made in a zero sum manner and not affect the overall size of the applicable Formula Approach Pool.

(h)                                 Board Review of Formula Approach.  If the Board or the Committee determines that the Formula Approach results in compensation levels that do not appropriately reflect the Company’s underlying performance, then the Board or the Committee may terminate the Formula Approach or make adjustments to it that it deems appropriate.

SECTION 5.                            Payment of Awards.

5.1                                 Form of Award.  The Committee in its sole discretion shall determine for any Plan Year whether any Awards payable in that year shall be paid in cash or in restricted common shares of the Company or stock options.  Any Awards to be paid in restricted common shares or

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stock options shall be made under the Company’s 2002 Long Term Incentive and Share Award Plan (or any successor thereto).

5.2                                 Payout Period.  For each Plan Year, and subject to Section 5.3 hereof, unless otherwise determined by the Committee, Awards under the Target Bonus Approach and the Formula Approach shall be paid over a four-year period as follows:  40% shall be paid within three months of the end of such Plan Year, and 20% shall be paid within three months of the end of each of the next three calendar years.  If, following such initial four-year period relating to a given Plan Year, any additional amounts are owed to Eligible Employees under the Formula Approach as a result of recalculation of the applicable Formula Approach Pool, then such amounts shall be paid to such Eligible Employees when bonuses are next paid hereunder.  Notwithstanding the foregoing, junior employees subject to the Target Bonus Approach, as designated by senior management of the applicable business segment or unit, shall receive 100% of their Awards within three months following the end of each Plan Year, and the payment schedule for junior employees subject to the Formula Approach shall be determined by senior management.

5.3                                 Vesting.  Each Eligible Employee must be employed by the Company at the time of each payment of an Award unless terminated by the Company not for Cause or as a result of death or Permanent Disability.  In the event an Eligible Employee ceases to be an employee of the Company prior to the date an Award is paid (i) due to termination by the Company not for Cause or (ii) as a result of death or Permanent Disability, the Award shall become vested in full at the time of such termination of service and shall be paid when bonuses are next paid hereunder following such termination of employment in the form determined by the Committee.  If the Eligible Employee ceases to be an employee of the Company for any other reason prior to the date that an Award is paid, the Award shall be forfeited by the Eligible Employee and become the property of the Company.  For purposes hereof, service with any of the Subsidiaries shall be considered to be service with the Company.  Vested amounts shall reflect applicable carryforwards and Deficits, and terminated employees unvested amounts shall be removed from the applicable bonus pool.

SECTION 6.                            Non-Transferability.

No Award or rights under this Plan may be transferred or assigned other than by will or by the laws of descent and distribution.

SECTION 7.                            Amendments and Termination.

The Board may terminate the Plan at any time and may amend it from time to time, provided, however, that no termination or amendment of the Plan shall adversely affect the rights of an Eligible Employee or a beneficiary to a previously determined Award without the written consent of such Eligible Employee or beneficiary.

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SECTION 8.                            General Provisions.

8.1                                 Subsidiaries.  Any Subsidiary of the Company may, upon approval by the Committee, become an Employer under the terms of the Plan.  Notwithstanding any provision of the Plan to the contrary, benefits payable under the Plan to an Eligible Employee or his or her beneficiary shall be the obligation of the Employer who actually employs (or, in the case an Eligible Employee who is no longer employed by an Employer, last employed) the Eligible Employee; provided, however, that in the event the Eligible Employee’s employer fails to make a payment of benefits to the Eligible Employee or his or her beneficiary when due under the terms of the Plan, the Company (the parent company of the Employers) shall be obligated to make such benefit payments in accordance with the terms of the Plan.

8.2                                 Unfunded Plan.  The Plan shall be an unfunded incentive compensation arrangement.  Nothing contained in the Plan, and no action taken pursuant to the Plan, shall create or be construed to create a trust of any kind.  An Eligible Employee’s right to receive a bonus shall be no greater than the right of an unsecured general creditor of the Company.  All bonuses shall be paid from the general funds of the Employers, and no segregation of assets shall be made to ensure payment of bonuses.

8.3                                 Withholding.  The Company may provide for the withholding from any benefits payable under this Plan all Federal, state, city or other taxes as shall be required pursuant to any law or governmental regulation or ruling.

8.4                                 Excess Parachute Payments.

(a)                                  Notwithstanding any other provision of the Plan, in the event that the amount of payments or other benefits payable to any Eligible Employee under the Plan (including, without limitation, the acceleration of any payment or the accelerated vesting of any payment or other benefit), together with any payments, awards or benefits payable under any other plan, program, arrangement or agreement maintained by the Company or one of its affiliates, would constitute an “excess parachute payment” (within the meaning of Section 280G of the Code), the payments under this Plan shall be reduced (by the minimum possible amounts) until no amount payable to the Eligible Employee under the Plan constitutes an “excess parachute payment” (within the meaning of Section 280G of the Code); provided, however, that no such reduction shall be made if the net after-tax payment (after taking into account Federal, state, local or other income, employment and excise taxes) to which the Eligible Employee would otherwise be entitled without such reduction would be greater than the net after-tax payment (after taking into account Federal, state, local or other income, employment and excise taxes) to the Eligible Employee resulting from the receipt of such payments with such reduction.  If, as a result of subsequent events or conditions (including a subsequent payment or absence of a subsequent payment under the Plan or other plans, programs, arrangements or agreements maintained by the Company or one of its affiliates), it is determined that payments hereunder have

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been reduced by more than the minimum amount required under this Section 8.4, then an additional payment shall be promptly made to the Eligible Employee in an amount equal to the excess reduction.

(b)                                 All determinations required to be made under this Section 8.4, including whether a payment would result in an “excess parachute payment” and the assumptions to be utilized in arriving at such determinations, shall be made by an accounting firm designated by the Company (the “Accounting Firm”) which shall provide detailed supporting calculations both to the Company and the Eligible Employee as requested by the Company or the Eligible Employee.  All fees and expenses of the Accounting Firm shall be borne solely by the Company and shall be paid by the Company.  Except as set forth in the last sentence of Section 8.4(a) hereof, all determinations made by the Accounting Firm under this Section 8.4 shall be final and binding upon the Company and the Eligible Employee.

8.5                                 Hold Harmless.  No member of the Board of the Committee, nor any officer or employee of the Company acting on behalf of the Board or the Committee, shall be personally liable for any action, determination or interpretation taken or made with respect to the Plan, and all members of the Board or the Committee and all officers or employees or the Company acting on their behalf shall, to the extent permitted by law, be fully indemnified and protected by the Company in respect of any such action, determination or interpretation.

8.6                                 Other Benefits; No Right of Employment.  Nothing set forth in this Plan shall prevent the Board or the Committee from adopting other or additional compensation arrangements.  Neither the adoption of the Plan or any Award hereunder shall confer upon an Eligible Employee any right to continued employment.

8.7                                 Captions.  The captions preceding the sections and articles hereof have been inserted solely as a matter of convenience and in no way define or limit the scope or intent of any provisions of the Plan.

8.8                                 Governing Law.  The Plan shall be interpreted, construed and administered in accordance with the laws of the State of New York, without giving effect to principles of conflict of laws.

SECTION 9.                            Effective Date of Plan.

The Plan shall become effective as of January 1, 2003, and shall remain in effect until such time as it may be terminated pursuant to Section 7 hereof.

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Schedule I

Unless otherwise indicated, all capitalized terms used below have the meanings specified in the Plan.

“ROE” means, with respect to each of the Insurance Segment and the Reinsurance Segment for a given Plan Year, After-Tax Profit (Loss) divided by Equity.  For each Plan Year, ROE shall be recalculated annually during the Development Period relating to such Plan Year.

“After-Tax Profit (Loss)” means, with respect to each of the Insurance Segment and the Reinsurance Segment for a given Plan Year, the sum of (i) Underwriting Profit (Loss) and (ii) Investment Income, taxed based upon the actual effective tax rate of the Insurance Segment or Reinsurance Segment, as applicable.

“Cash Flow” means, with respect to the Insurance Segment and the Reinsurance Segment for a given Plan Year, net operating cash flow for such segment reflecting premiums collected, net of reinsurance, loss and loss adjustment expenses paid, underwriting expenses paid and all other operating expenses, including unallocated loss adjustment expenses, allocation of expenses from the Company and Arch Capital Services Inc., federal excise taxes, applicable income taxes and costs of letters of credit, but excluding bonuses payable to Eligible Employees (“Operating Expenses”).  For such purposes, CAT Business shall be reflected in the Formula Approach in the manner described in Section 4.3(f) of the Plan.

“Equity” means, with respect to each of the Insurance Segment and the Reinsurance Segment for a given Plan Year, the amount of capital allocated to each such segment as recommended by senior management and determined by the Committee.

“Investment Income” means, with respect to the Insurance Segment and the Reinsurance Segment for a given Plan Year, the sum of investment income, compounded as per the applicable U.S. treasury security, on:

(i)                                     Equity, calculated at a rate equal to the average rate earned on the investment portfolios of the Company and its Subsidiaries during the initial 12-month calendar year period included in the Plan Year, net of investment expenses relating to such portfolios; and

(ii)                                  Cash Flow, calculated at the following rates:  (A) with respect to all business other than property business, the average risk free rate equal to the yield on a U.S. Treasury security with a duration equal to estimated weighted average duration of the underwriting (or policy) year liabilities, net of estimated investment expenses relating to a portfolio of U.S. Treasury securities, and, (B) with respect to property business, the average risk free rate equal to the yield on a U.S. Treasury security with a one year duration, net of estimated investment expenses relating to a portfolio of U.S. Treasury securities.

“Underwriting Profit (Loss)” reflects, with respect to each of the Insurance Segment and the Reinsurance Segment for a given Plan Year, (i) net premiums earned, fee income, losses and loss adjustment expenses and acquisition expenses attributable to Policies having an inception or renewal date within the Plan Year and (ii) all other Operating Expenses incurred during the initial 12-month calendar year period included in the Plan Year.  For such purposes, CAT Business shall be reflected in the Formula Approach in the manner described in Section 4.3(f) of the Plan.

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