EMPLOYMENT AGREEMENT

Exhibit 10.35

EMPLOYMENT AGREEMENT

THIS AGREEMENT, made and entered into as of the 22nd day of May, 1995 by and between ACE Limited, a Cayman Islands corporation, the “Company”) and Brian E. Dowd (the “Executive”).

WHEREAS, the Company desires to offer employment to the Executive under the terms and conditions set forth below; and

WHEREAS, the Executive wishes to accept such employment under such terms and conditions.

NOW, THEREFORE, in consideration of the promises and mutual covenants contained herein and for other good and valuable consideration, the Company and the Executive (the “Parties”) hereby agree as follows:-

1. Employment

The Company hereby employs the Executive, and the Executive hereby accepts employment with the Company, for the term of this Agreement as set forth in Section 2 below, in the position and with the duties and responsibilities set forth in Section 3 below, and upon such other terms and conditions as are hereinafter stated.

2. Term and Place of Performance

(a) The term of the Agreement shall commence as of the date first above written (the “Commencement Date”) and shall continue through the close of business on May 22nd, 1998, subject to the terms and conditions of this Agreement. This Agreement shall automatically renew for a one-year term effective May 22nd, 1998 and each succeeding May 1st thereafter, unless the Chief Executive Officer of the company notifies the Executive in writing at least 30 days prior to any such May 22nd of its intention not to renew the Agreement.

(b) Except for travel required from time to time in the conduct of the Company’s business or the business of any of the Company’s affiliates, the Executive’s services under this Agreement shall be performed in Bermuda. The obligations of the Company under this Agreement shall be contingent upon the issuance of a work permit by the Government of Bermuda and any other permits required by the Government of Bermuda. Failure to obtain said permits shall void this Agreement. Once obtained, the maintenance of such permits throughout the term of this Agreement shall be a continuing condition to the Company’s obligations under this Agreement. However, if despite the Executive’s best efforts to maintain the permits, they are terminated or revoked by the Government of Bermuda through no fault of the Executive, then the Executive shall be entitled to the benefits provided for termination without Cause under Section 10(d).

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3. Positions, Duties, and Time Devoted to the Companies & Its Affiliates

(a) During the term of the Agreement, the Executive shall be employed as Vice President, Underwriting of the Company, with such powers and duties normally attendant to such offices and such other duties as may be assigned to the Executive. Executive shall answer to and be subject to the direction of the Executive Vice President, Underwriting, or his designee.

(b) The Executive agrees to remain in the employ of the Company during the term of this Agreement, to devote his full business time exclusively to the business affairs of the Company, and to perform his duties faithfully and efficiently. Subject to the demands of his position with the Company, the Executive shall be permitted to:

(i) deliver lectures and fulfill speaking engagements; and

(ii) engage in charitable and community activities; provided, however, that any expenses, such as for travel, incurred by the Executive in connection with such activities shall be for the personal account of the Executive and shall not be reimbursed by the Company.

4. Salary

For services rendered by the Executive to the Company during the term of this Agreement while he is employed by the Company, the Executive shall be paid a minimum annual base salary at a rate of $115,000. The annual base salary shall be paid on a monthly basis by ACE.

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5. Sign-on Bonus & Moving Allowance

The Company will pay the Executive $15,000 as a moving allowance and will reimburse the Executive for reasonable moving expenses for household goods in relocating to Bermuda.

6. Annual Performance Incentive Plan

Subject to the terms and conditions of this Agreement, the Executive shall be eligible to receive an Annual Performance Incentive Award in an amount determined by the Compensation Committee of the Board of Directors.

The amount of the Annual Performance Incentive Award, if any, payable to the Executive after his termination of employment shall be determined in accordance with Section 10. Any Annual Performance Incentive Award payable to the Executive pursuant to this Section 6 shall be paid to him at such time and in such form as such awards are typically paid to other employees of ACE.

7. Stock Options

Subject to approval by the Company’s Board of Directors, the Company shall issue to Executive options to purchase 5,000 shares of the Company’s stock at the market price in effect at the close of trading the first trading day following approval by the Board of Directors. If issued, said options shall be subject to all the terms and conditions set forth in the Company’s Equity Linked Incentive Plan.

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8. Employee Benefits

(a) During the term of his employment, the Executive shall be entitled to participate in the Company’s retirement plan, supplemental retirement plan, hospitalization plan, major medical plan, dental plan, group-term life insurance plan, accidental death and dismemberment plan, and such other employee benefits programs as in effect from time to time in which the Company’s employees may participate, subject to satisfaction of all eligibility requirements of general applicability and all other terms and conditions of the plans; (provided, however, that, except for the Equity Linked Incentive Plan, the Executive shall not be entitled to participate in any of the Companies’ bonus plans.)

(b) The Executive shall be entitled to four weeks of vacation in a full calendar year. Unused vacation days shall expire as of the last day of each one year period and may not be accumulated, carried forward or redeemed for other compensation.

9. Business Expense Reimbursement Accommodation Other Perquisites

(a) During the term his employment, the Executive shall be entitled to be reimbursed by ACE for all reasonable out-of-pocket travel and entertainment expenses incurred by him in performing services under this Agreement, provided that the Executive submits reasonable documentation with respect to such expenses.

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(b) During the term of his employment, the Executive shall be entitled to be reimbursed for membership in one Bermuda club of his choice.

(c) During the term of the Executive’s employment, the Company will reimburse the Executive for three round trip tourist class airfares per year between Bermuda and Chicago, Illinois for him and his immediate family upon submission of reasonable documentation that the fares were incurred.

(d) During the term of his employment, the Executive shall be entitled to be reimbursed for reasonable costs incurred in preparing his United States income taxes.

(e) The Executive shall be indemnified by the Companies in accordance with their Articles of Incorporation.

10. Termination of Employment

(a) Termination Due to Death. In the event of the Executive’s death during the term of his employment hereunder, the estate or other legal representative of the Executive shall be entitled to:

(i) continuation of the Executive’s annual base salary provided in Section 4 above through the last day of the month in which the Executive dies;

(ii) any rights and benefits available under any employee benefits plans, policies, and practices of the Companies, determined in accordance with the applicable terms and provisions of such plans, policies, and practices as in effect on the date of the Executive’s death.

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(b) Termination Due to Disability. In the event the Executive’s employment by the Companies is terminated because he is adjudged by the Compensation Committee to be disabled within the meaning of the Company’s long-term disability plan, the Executive shall be entitled to:

(i) continuation of the annual base salary provided in Section 4 above through the last day of the month in which the Executive’s employment with the Company terminates due to disability;

(ii) any rights and benefits available under any employee benefit plans, policies, and practices of the Company, determined in accordance with the applicable terms and provisions of such plans, policies, and practices as in effect on the date of the Executive’s termination of employment.

(c) Termination by the Companies for Cause.

(i) The employment of the Executive under this Agreement may be terminated by the Company for Cause. For purposes of this Agreement, “Cause” shall mean:

(A) commission by the Executive of a felony involving moral turpitude;

(B) violations of Section 11 or 12 of this Agreement; or

(C) the Executive, in carrying out his duties, has been guilty of (1) neglect, or (2) misconduct; provided, however, that any act, or failure to act, by the Executive shall not constitute Cause for purposes of this Section 10(c)(i)(c) if such act or failure to act, was committed, or omitted, by the Executive in good faith and in a manner he reasonably believed to be in the best interests of the Company.

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(ii) In the event of a termination of the Executive’s employment for Cause under Section 10(c)(i) above, the Executive shall be entitled only to:

(a) continuation of the annual base salary provided in Section 4 above through the date on which termination for Cause occurs; and

(b) any other rights and benefits, if any, available under employee benefit plans, policies, and practices of the Company, determined in accordance with the applicable terms and provisions of such plans, policies, and practices, as in effect on the date of her termination of employment.

(d) Termination Without Cause

(i) Anything in this Agreement to the contrary notwithstanding, the Executive’s employment may be terminated without Cause as provided in this Section 10(d). Termination without Cause shall mean a termination of the Executive’s employment by the Company, other than a termination due to death as described in Section 10(a) above, disability as described in Section 10(b) above, or a termination for Cause as described in Section 10(c) above.

ii) In the event there is a termination without Cause of the Executive’s employment, the Executive shall be entitled to:

(A) continuation of the annual base salary provided in Section 4 above until the date which is twenty-four months after the last day of the month in which such termination occurs; provided, however, that payments pursuant to this Section 1.0(d)(ii)(A) are subject to the provisions of Section 13;

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(B) any Annual Performance Incentive Bonus for a completed fiscal year which has not yet been paid to the Executive, which bonus shall be paid in accordance with Section 6;

(C) any Equity Linked Incentive Bonus calculated and payable pursuant to the provisions of the Equity Linked Incentive Plan which has not yet been paid to the Executive;

(D) continuation of coverage under the employee benefit plans of the Company in which the Executive was participating at the time of his termination of employment for the period of salary continuation under Section 10(d)(A) above; provided, however, that (1) except as required by applicable law, any such continued coverage shall terminate upon the subsequent full-time employment of the Executive, and (2) if the Company is unable to continue such coverage, then they shall provide the Executive with economically equivalent employee benefits to the extent such benefits are reasonably available; and

(E) any other rights and benefits available under employee benefit plans, policies, and practices of the Company, determined in accordance with the applicable terms and provisions of such plans, policies, and practices, as in effect on the date of his termination of employment.

(iii) At the discretion of the Compensation Committee, the present value of any amounts payable to the Executive in accordance with Section 10(d)(ii)(A) above may be paid to the Executive in a lump sum. The interest rate used in determining the present value shall be the interest rate on one-year United States Treasury Bills at the auction of such instruments nearest in time to the date of the Executive’s termination of employment

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under this Section 10(d). Any such lump sum payment by the Company to the Executive shall not affect the obligation of the Companies as otherwise provided in Section 10(d)(ii)(D) above to provide continuation coverage under the employee benefit plans.

(e) Voluntary Termination by the Executive

The Executive may voluntarily terminate his employment with the Company at any time prior to the expiration of the term of this Agreement. Such termination shall constitute a voluntary termination and, in such event, the Executive shall be limited to the same rights and benefits as applicable to the termination for Cause, as described in Section 10(c) above.

11. Noncompetition

During the term of the Executive’s employment and for a period of 24 months following the termination of his employment for any reason, the Executive shall not, directly or indirectly, whether as an employee, consultant, partner, principal, agent, distributor, representative, stockholder (except as a less than one percent stockholder of a publicly traded company or a less than five percent stockholder of a privately held company) or otherwise, engage, within the United States, Bermuda, or the Cayman Islands, if such activities involve insurance or reinsurance of United States based entities or exposure in any activities that are competitive with the Property insurance business then being conducted by the Company and which, during the period covered by the Executive’s employment, were either (1) conducted by the Company, or (2) actively being developed by the Company. For as long as the above described restrictions on competition apply, the Executive shall not

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hire any employee or former employee of ACE Limited or any present or former affiliate company of ACE Limited nor encourage any employee of the Company to leave the employ of the Company.

12. Confidential Information

The Executive covenants that he shall not, without the prior written consent of the Chief Executive Officer use, or disclose to any person (other than an employee of either of the Company, or other person to whom disclosure is necessary to the performance by the Executive of his duties in the employ of the Company) any confidential or proprietary information about the Company or their business, unless and until such information has become known to the public generally (other than as a result of unauthorized disclosure by the Executive). The foregoing covenants by the Executive shall be without limitation as to time and geographic applications.

13. Remedy for Violation of Noncompetition or Confidential Information Provisions

Without intending to limit the remedies available to the Company for the breach of any of the Executive’s covenants in Sections 11 and 12, the Executive acknowledges and agrees that damages at law are an insufficient remedy for the Company and that, accordingly, the Company shall be entitled to apply for and obtain injunctive relief in any court of competent jurisdiction to restrain the breach or threatened breach, or otherwise specifically enforce, any or all of said covenants. The Parties acknowledge that each of the covenants contained in Sections 11 and 12 is an essential element of this Agreement. If any covenant or term of Section 11 or 12 or any portion thereof of this Section 13, is determined to be invalid or unenforceable in any

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instance, such determination shall not prevent the reassertion thereof with respect of any other breach or violation. If, in any proceeding, a court (or other tribunal) refuses to enforce the covenants contained in Section 11 or 12 or this Section 13 because such covenants cover too extensive a geographic area or too long a period of time, any such covenant shall be deemed amended to the extent (but only to the extent) required by law to permit its enforceability hereunder. Notwithstanding anything contained in this Agreement to the contrary, in the event that the Executive’s employment is terminated without Cause (as defined in Section 10(d)(i)) and the Company reasonably determines that the Executive has violated Section 11 or 12 of this Agreement, then the Companies shall be entitled to discontinue any payments or benefits that would otherwise be provided under Section 10(d) and the Executive shall forfeit his rights to the same.

14. Withholding

Anything in this Agreement to the contrary notwithstanding all payments required to be made by the Company hereunder to the Executive shall be subject to withholding of such amounts relating to taxes as the Company may reasonably determine they are required to withhold pursuant to any applicable law or regulation. In lieu of withholding such amounts, in whole or in part, the Company may, in their sole discretion, accept other provision for payment of taxes as required by law, provided they are satisfied that all requirements of law affecting their responsibilities to withholding such taxes have been satisfied.

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15. Arbitration of All Disputes

Subject to the provisions of Section 13, any controversy or claim arising out of or relating to this Agreement or the breach thereof shall be settled by arbitration in the City of Hamilton in accordance with the law of Bermuda by three arbitrators appointed by the Parties. If the Parties cannot agree on the appointment of the arbitrators, one shall be appointed by the Company and one by the Executive and the third shall be appointed by the first two arbitrators. If the first two arbitrators cannot agree on the appointment of a third arbitrator, then the third arbitrator shall be appointed by the Chief Justice of the Supreme Court of Bermuda. The arbitration shall be conducted in accordance with the rules of the Arbitration Act, 1986, as amended, except with respect to the selection of the arbitrators which shall be as provided in this Section 15. Judgment upon the award rendered by the arbitrators may be entered in any court having jurisdiction thereof. The arbitrators’ fees and any expenses relating to the arbitration (other than the Parties’ own legal fees and expenses) shall be shared equally by the parties.

16. Entire Agreement

This Agreement contains the entire agreement between the Parties concerning the subject matter hereof and supercedes all prior agreements, undertakings, discussions, negotiations, and undertakings, whether written or oral, between the Company and the Executive with respect thereto.

17. Assignability ability: Binding Nature

This Agreement shall be binding upon and inure to the benefit of the Parties and their respective successors, heirs, and assigns. No rights or obligations of the Executive under this Agreement may be assigned or

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transferred by the Executive, other than his rights to receive salary and bonuses hereunder which may be transferred by will or operation of law subject to the limitations of this Agreement. No rights or obligations of the Company under this Agreement may be assigned or transferred by the Company except that such rights or obligations may be assigned or transferred pursuant to a merger or consolidation in which the Company is not the continuing entity, or the sale or liquidation of all or substantially all of the assets of the Company, provided that that assignee or transferee is the successor to all or substantially all of the assets of the Company and such assignee or transferee assumes the liabilities, obligations, and duties of the Company as contained in this Agreement, either contractually or as a matter of law.

18. Amendment of Waiver

No provision in this Agreement may be amended or waived unless such amendment or waiver is (1) agreed to in writing, and (2) the agreement is signed by the Executive and by the Assistant Secretary. No waiver by any party hereto of any breach by any other party of any condition or provision of this Agreement to be performed by such other party shall be deemed a waiver of a similar or dissimilar condition or provision at the same or any prior or subsequent time.

19. 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 sent by certified or registered mail, postage prepaid, return receipt requested, duly addressed to the party concerned at the address

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indicated below to such changed address of which such party may subsequently by similar process give notice:

20. Severability

In the event that any provision or portion of this Agreement shall be determined to be invalid or unenforceable for any reason, in whole or in part, the remaining provisions of this Agreement shall be unaffected thereby and shall remain in full force and effect to the fullest extent permitted by law.

21. Survivorship

The respective rights and obligations of the parties shall survive any termination of this Agreement to the extent necessary to the intended preservation of such rights and obligations.

22. References

In the event of the Executive’s death or a judicial determination of his incompetence, reference in this Agreement to the Executive shall be deemed, where appropriate, to refer to his estate or other legal representative. All statements of or references to dollar amounts in this Agreement shall mean lawful money of the United States of America.

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23. Governing Law

This Agreement shall be governed by and construed and interpreted in accordance with the laws of Bermuda, without reference to the principles of conflict of laws.

24. Headings

The headings of paragraphs contained in this Agreement are for convenience only and shall not be deemed to control or affect the meaning or construction of any provision of this Agreement.

25. Counterparts

This Agreement may be executed in one or more counterparts.

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

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