Exhibit (a)(1)(K) WHITE MOUNTAINS INSURANCE GROUP, LTD. OFFER TO PURCHASE FOR CASH UP TO 1,500,000 OF ITS COMMON SHARES AT $165.00 NET PER SHARE THE OFFER, PRORATION PERIOD AND WITHDRAWAL RIGHTS WILL EXPIRE AT 12:00 MIDNIGHT, NEW YORK CITY TIME, ON MONDAY, SEPTEMBER 18, 2000, UNLESS THE OFFER IS EXTENDED. August 21, 2000 To Participants of the Allianz Asset Accumulation Plan (the "AAAP"): Enclosed for your consideration is the Offer to Purchase dated August 21, 2000, of White Mountains Insurance Group, Ltd., a company organized under the laws of Bermuda (the "Company"), and a related specimen Letter of Transmittal (which together constitute the "Offer"), pursuant to which the Company is offering to purchase up to 1,500,000 of its outstanding Common Shares, par value $1.00 per share (the "Shares"), for cash at $165.00 per Share net to the seller, upon the terms and subject to the conditions set forth in the Offer. The Company may elect, but shall not be obligated, to purchase additional Shares pursuant to the Offer. The Offer to Purchase and a specimen Letter of Transmittal are being forwarded to you as the beneficial owner of Shares held by The Northern Trust Company as Trustee ("Trustee") of the Fireman's Fund Insurance Company Master Retirement Savings Trust ("Trust") in your account but not registered in your name. A TENDER OF SUCH SHARES CAN BE MADE ONLY BY THE TRUSTEE AS THE HOLDER OF RECORD AND ONLY PURSUANT TO YOUR INSTRUCTIONS. THE TRUSTEE WILL NOT TENDER ANY SHARES OF WHITE MOUNTAINS INSURANCE GROUP, LTD. HELD BY THE PLAN FOR WHICH NO PARTICIPANT INSTRUCTIONS ARE TIMELY RECEIVED UNLESS IT DETERMINES THAT IT IS LEGALLY OBLIGATED TO DO SO. THE LETTER OF TRANSMITTAL IS FURNISHED TO YOU FOR YOUR INFORMATION ONLY AND CANNOT BE USED BY YOU TO TENDER SHARES HELD BY US FOR YOUR ACCOUNT. YOUR ATTENTION IS CALLED TO THE FOLLOWING: 1. The tender price is $165.00 per Share net to you in cash. 2. The Offer is not conditioned upon any minimum number of Shares being validly tendered. 3. Tendering shareholders will not be obligated to pay brokerage commissions or, subject to Instruction 6 of the Letter of Transmittal, transfer taxes on the purchase of Shares by the Company pursuant to the Offer. 4. The Offer and the Proration Period expire at 12:00 midnight, New York City time, on Monday, September 18, 2000, unless extended (the "Expiration Date"). 5. The Offer is subject to the terms and conditions set forth in the Offer to Purchase, which you should read carefully. In order to be assured that your instructions to the Trustee are followed, your instruction form must be completed, signed, dated and received by the Trustee NO LATER THAN 11:00 P.M. NEW YORK TIME (10:00 P.M. CHICAGO TIME) ON THURSDAY, SEPTEMBER 14, 2000. This time is two business days plus one hour prior to the expiration of the Offer, which is scheduled to expire at 12:00 Midnight New York Time (11:00 p.m. Chicago Time) on September 18, 2000. If the expiration of the Offer is extended beyond its scheduled expiration time by the Company, the time by which the Trustee must receive your instruction will be extended automatically to two business days plus one hour prior to such extended expiration time. PLEASE REMEMBER TO RETURN YOUR INSTRUCTION FORM TO THE TRUSTEE IN THE ENCLOSED ENVELOPE, RATHER THAN TO THE COMPANY, EQUISERVE TRUST COMPANY, OR ANY OTHER PARTY. As described in the Offer to Purchase, if more than 1,500,000 (or such greater number, as the Company may elect to purchase) Shares are validly tendered on or prior to the Expiration Date, subject to the terms and conditions of the Offer, the Company, upon the terms and subject to the conditions of the Offer, will purchase all Shares validly tendered in the following order of priority: (a) first, all Shares properly tendered and not withdrawn before the Expiration Date by any shareholder who owned beneficially as of the close of business on August 14, 2000, and who continues to own beneficially until the Expiration Date, an aggregate of fewer than 100 Shares, including all Shares held by you through the AAAP or otherwise, and who tenders all Shares beneficially owned by such shareholder (PARTIAL TENDERS WILL NOT QUALIFY FOR THIS PREFERENCE); and (b) then, after purchase of all the foregoing Shares, all other Shares properly tendered and not withdrawn before the Expiration Date, on a pro rata basis if necessary (with appropriate adjustments to avoid purchase of fractional Shares). The Offer is not being made to (nor will tenders be accepted from or on behalf of) holders of Shares residing in any jurisdiction in which the making of the Offer or the acceptance thereof would not be in compliance with the securities or Blue Sky laws of such jurisdiction.