<PAGE>

                                                                   EXHIBIT 10.20

                                 ADDENDUM NO. 2

                                     TO THE

                        QUOTA SHARE REINSURANCE AGREEMENT
                           DATED AS OF MARCH 27, 2003

              (HEREINAFTER REFERRED TO AS THE "ORIGINAL AGREEMENT")

                                     BETWEEN

                            PLATINUM RE (UK) LIMITED

                   (HEREINAFTER REFERRED TO AS THE "COMPANY")

                                       AND

                       PLATINUM UNDERWRITERS BERMUDA, LTD

                  (HEREINAFTER REFERRED TO AS THE "REINSURER")

WHEREAS, the Reinsurer and the Company are parties to the Original Agreement.

NOW THEREFORE, effective from the Commencement of the Original Agreement, the
parties hereto hereby agree to amend the said agreement as follows:

      Article 4 - PREMIUMS AND COMMISSIONS. The existing clause shall be deleted
      in its entirety and replaced with the following:

      "As premium for the reinsurance provided hereunder, the Retrocedant shall
      retrocede to the Retrocessionaire fifty-five percent (55%) of the Gross
      Net premium ceded to the Retrocedant under the Reinsurance Contracts.

      The Retrocessionnaire shall pay a ceding commission equal to the sum of
      (1) applicable ceding and other commissions, (2) brokerage, (3) taxes, and
      (4) other expenses associated with underwriting the Reinsurance Contracts.

      Other expenses associated with underwriting shall be limited to a maximum
      of 10 percent (10%) of the Gross Net Premium ceded to the Retrocedant
      under the Reinsurance Contracts.

      Gross Net Premium is defined as the total sum of all premiums associated
      with Reinsurance Contracts ceded to the Retrocedant, less: (1) return
      premiums, and (2) ceded reinsurance premium."

                                                                     Page 1 of 2

<PAGE>

      Article 8 - REPORTS AND REMITTANCES. The existing clause shall be deleted
      in its entirety and replaced with the following:

      "The retrocedant shall render separately, monthly statements of account,
      in arrears, in respect of each year of account, showing the total of all
      premiums, written, paid loss and loss adjustment expenses, allowances,
      commissions, and underwriting expenses relevant to that month. Such
      accounts shall be rendered, as soon as possible after the close of the
      relevant month with the balance payable within 45 days after the end of
      the respective month.

      The retrocedant shall normally debit the retrocessionaire with their
      proportionate share of paid losses and loss adjustment expenses in the
      monthly accounts rendered. The retrocedant may, however, at their
      discretion, request the retrocessionaire to make immediate payment for
      their proportion of any settled loss in excess of (pound)2 million for any
      one loss relating to this agreement; provided that the retrocessionaire
      shall have the right to deduct from any such payment any sums due to the
      retrocessionaire under this agreement for any agreement renewing or
      replacing this agreement.

      In addition, the Retrocedant will furnish the Retrocessionaire a quarterly
      statement showing the unearned premium, the total reserves for outstanding
      losses including loss adjustment expense, a breakdown for paid and
      outstanding catastrophe losses and loss adjustment expense, and such other
      information as may be required by the Retrocessionaire for completion of
      its annual statements or other filings."

All other terms and conditions of the Original Agreement remain unchanged.

In Witness Whereof, the parties hereto have caused this Addendum No.2 to be
executed by their duly authorized representatives.

                                           Platinum Underwriters Bermuda, Ltd.

                                           By: /s/ Francois Bertrand
                                               -------------------------------
                                           Name: Francois Bertrand
                                           Title: Senior Vice President

                                           Platinum Re (UK) Limited

                                           By: /s/ Les Waters
                                               -------------------------------
                                           Name: Les Waters
                                           Title: Senior Underwriter

                                                                     Page 2 of 2