<PAGE>

                                                                 EXHIBIT 10.36

                  FIRST AMENDMENT, dated as of November 1, 2002 (the
"Amendment"), to the Investment Agreement, dated as of September 20, 2002 (the
"Investment Agreement"), by and among Platinum Holdings Ltd., a Bermuda company
(the "Company"), The St. Paul Companies, Inc., a Minnesota corporation ("St.
Paul"), and RenaissanceRe Holdings Ltd., a Bermuda company (the "Purchaser").
Each capitalized term used and not otherwise defined herein shall have the
meaning assigned to such term in the Investment Agreement.

                  WHEREAS, the Company, St. Paul and the Purchaser desire to
modify the Investment Agreement in accordance with the provisions of Section
10.4 thereof.

                  NOW, THEREFORE, in consideration of the mutual agreements
herein contained and other good and valuable consideration, the sufficiency and
receipt of which are hereby acknowledged, the parties hereto agree as follows:

                  Section 1.        Amendments to the Investment Agreement.

                  (a)      The last sentence of Section 5.1 of the Investment
Agreement is hereby amended and restated as follows:

                           The Chief Executive Officer or the Treasurer of the
                  Company and the Chief Executive Officer, Chief Financial
                  Officer or any Executive Vice President of St. Paul each shall
                  have delivered at the Closing a certificate stating that each
                  of the respective conditions specified in the preceding
                  sentence has been fulfilled, which certificates shall also be
                  delivered at any Second Closing.

                  (b)      Section 1.1 of the Transfer Restrictions,
Registration Rights and Standstill Agreement attached as Exhibit A to the
Investment Agreement is hereby amended by adding the following definitions in
the appropriate alphabetical order:

                           "Purchase Contract" means the contract to purchase
                  Common Shares issued as part of the Units."

                           "Purchase Contract Agreement" means the purchase
                  contract agreement between the Company and JPMorgan Chase
                  Bank, as purchase contract agent."

                           "Units" means Company's equity security units having
                  a stated amount of $25 per Unit."

                  (c)      The last sentence of Section 5(b) of the Transfer
Restrictions, Registration Rights and Standstill Agreement attached as Exhibit A
to the Investment Agreement is hereby amended and restated as follows:

                           Purchaser shall have ten days from the date of
                  receipt of any such notice to agree to purchase up to
                  Purchaser's pro rata share of New Securities specified above
                  for the same price paid to the Company in connection with such
                  Dilutive Transaction (i.e., less underwriting discounts and
                  commissions) by giving written notice to the Company and
                  stating therein the quantity of New Securities to be purchased
                  provided, however, that in the connection with an Early
                  Settlement (as

<PAGE>

                  such term is defined in the Purchase Contract Agreement) of
                  the Purchase Contracts pursuant to Section 5.10 of the
                  Purchase Contract Agreement, this Section 5(b) shall not
                  apply, but the Company shall give the Purchaser prompt written
                  notice of such Early Settlement.

                  (d)      The first paragraph of the RenaissanceRe Option
Agreement attached as Exhibit B to the Investment Agreement is hereby amended by
(i) inserting "AND EXCEPT TO THE EXTENT PERMITTED HEREIN" immediately following
the word "APPROVALS" in the second sentence thereof, and (ii) deleting the
reference to "SECTION 6(C)" in the final sentence thereof and inserting "SECTION
6" in replacement therefor.

                  (e)      The last sentence of Section 3(e) of the
RenaissanceRe Option Agreement attached as Exhibit B to the Investment Agreement
is hereby amended and restated as follows:

                           The "Initial Dividend" means the distributions
                  described in items (i) and (ii) above per Common Share paid by
                  the Company to all or substantially all holders of its Common
                  Shares during the 2003 calendar year as determined by the
                  Company's Board of Directors, up to a maximum of $0.44 per
                  Common Share.

                  (f)      Section 6(a) of the RenaissanceRe Option Agreement
attached as Exhibit B to the Investment Agreement is hereby amended by inserting
the following sentence immediately following the first sentence thereof:

                           Notwithstanding anything to the contrary in this
                  Agreement, RenRe may, at any time, assign or otherwise
                  transfer, dispose or encumber the RenRe Option or the RenRe
                  Option Shares in whole or in part to any direct or indirect
                  wholly owned subsidiary of RenRe, provided that such
                  transferee shall enter into an option agreement with the
                  Company that is substantially identical to this Agreement.

                  Section 2.        Miscellaneous.

                  (a)      This Amendment shall be governed by and construed in
accordance with the laws of the State of New York, without regard to the
conflicts of laws rules of such State. This Amendment may be executed in one or
more counterparts, which together will constitute a single agreement.

                  (b)      The captions herein are included for convenience of
reference only and shall be ignored in the construction or interpretation
hereof.

                  (c)      This Amendment may not be amended nor may any
provision be waived except by a writing signed, in the case of an amendment, by
each party hereto and, in the case of a waiver, by the party against whom the
waiver is to be effective. Except as otherwise permitted pursuant to the
Investment Agreement, this Amendment is not assignable by any of the parties
without the prior written consent of the other parties. This Amendment shall be
binding upon and inure to the benefit of the parties hereto, any subsidiary to
whom the Shares are delivered pursuant hereto, and their respective successors
and permitted assignees.

                                       2

<PAGE>

                  (d)      The Investment Agreement, as amended hereby, is and
shall continue to be in full force and effect and is hereby in all respects
ratified and confirmed. Except as expressly modified and amended hereby, all of
the terms, provisions and conditions of the Investment Agreement shall remain
unchanged and in full force and effect. On and after the effective date of the
amendments to the Investment Agreement set forth above, each reference in the
Investment Agreement (including the exhibits and schedules thereto) shall mean
and be a reference to the Investment Agreement as amended hereby.

                                       3

<PAGE>

                  IN WITNESS WHEREOF, the parties hereto have caused this
Amendment to be duly executed by their respective authorized officers as of the
day and year first above written.

                                            RENAISSANCERE HOLDINGS LTD.

                                            By: /s/ John M. Lummis
                                                ------------------------------
                                            Name:  John M. Lummis
                                            Title: Executive Vice President and
                                                   Chief Financial Officer

                                            PLATINUM UNDERWRITERS HOLDINGS,
                                            LTD.

                                            By: /s/ Jerome T. Fadden
                                                ------------------------------
                                            Name:  Jerome T. Fadden
                                            Title: President and Chief
                                                   Executive Officer

                                            THE ST. PAUL COMPANIES, INC.

                                            By: /s/ Thomas A. Bradley
                                                ------------------------------
                                            Name:  Thomas A. Bradley
                                            Title: Executive Vice President and
                                                   Chief Financial Officer