Document:

<PAGE>
                                                                   Exhibit 10.34

C L I F F O R D                                    LIMITED LIABILITY PARTNERSHIP
C H A N C E

                      ALLIED WORLD ASSURANCE COMPANY, LTD.

                                   AS BORROWER

                                       AND

                                BARCLAYS BANK PLC

                                    AS ISSUER

                         ------------------------------

                           GLOBAL AMENDMENT AGREEMENT

                         ------------------------------
<PAGE>
                                    CONTENTS

<Table>
<Caption>
CLAUSE                                                                      PAGE
<S>                                                                     <C>
  1.  Definitions And Interpretation ...................................       1

  2.  Representations ..................................................       1

  3.  Amendments .......................................................       2

  4.  Continuity And Further Assurance .................................       3

  5.  Conditions And Confirmations ....................................        3

  6.  Fees, Costs And Expenses .........................................       3

  7.  Miscellaneous ....................................................       4

Schedule 1  CONDITIONS PRECEDENT .......................................       5
</Table>
<PAGE>
THIS AGREEMENT (the "Agreement") is made as of January 11, 2005 among:

(1)   ALLIED WORLD ASSURANCE COMPANY, LTD., a corporation organized under the
      laws of Bermuda, as Borrower; and

(2)   BARCLAYS BANK PLC, as Issuer.

(A)   WHEREAS, pursuant to a letter of credit issuance facility agreement dated
      as of 31 December 2003 (as amended, increased or otherwise modified from
      time to time, the "ORIGINAL CREDIT AGREEMENT") between, Allied World
      Assurance Company, Ltd., as Borrower and Barclays Bank plc, as Issuer, the
      Issuer issued certain letters of credit in accordance with the terms of
      the Original Credit Agreement.

(B)   WHEREAS, pursuant to a Security Agreement dated as of 31 December 2003 (as
      amended or otherwise modified from time to time, the "SECURITY AGREEMENT")
      by Allied World Assurance Company, Ltd in favor of Barclays Bank plc, as
      Issuer, the Borrower granted a security interest in the Collateral (as
      defined therein) to the Issuer.

(C)   WHEREAS the parties desire to extend the tenure of the Credit Agreement
      and make certain other amendments to the documents described above, all as
      set out below.

IT IS AGREED as follows:

1.    DEFINITIONS AND INTERPRETATION

1.1   DEFINITIONS

      In this Agreement:

      "AMENDED AGREEMENT" means the Original Credit Agreement as amended by this
      Agreement.

      "EFFECTIVE DATE" shall have the meaning given to it in Clause 5.1.

1.2   INCORPORATION OF DEFINED TERMS

      Terms not otherwise defined in this Agreement shall have the same meaning
      as set forth in the Original Credit Agreement.

1.3   CLAUSES

      (a)   In this Agreement any reference to a "Clause" or "Schedule" is,
            unless the context otherwise requires, a reference to a Clause or
            Schedule of this Agreement.

      (b)   Clause and Schedule headings are for ease of reference only.

2.    REPRESENTATIONS

      The Borrower repeats the representations set out in Clause 5
      (Representations and Warranties) of the Original Credit Agreement as if
      each reference in those

                                     - 1 -
<PAGE>
      representations to "this Agreement" includes a reference to (a) this
      Agreement and (b) the Amended Agreement.

3.    AMENDMENTS

3.1   AMENDMENT OF THE ORIGINAL CREDIT AGREEMENT

      With effect from the Effective Date:

      3.1.1 the Original Credit Agreement shall be amended as follows:

            (a)   The definition of "LC Facility Termination Date" shall be
                  deleted in its entirety and replaced with " "LC FACILITY
                  TERMINATION DATE" means December 31, 2005."

            (b)   The definition of "Permitted Terminations" is added to Section
                  1 in the proper alphabetical order and shall read in its
                  entirety as follows:

                  "PERMITTED TERMINATIONS" means the termination of the
                  following material contracts:

                  (i)   Each of the Surplus Lines Program Administrator
                        Agreements, dated as of December 28, 2001, between
                        Allied World Assurance Company (U.S.) Inc., f/k/a
                        Commercial Underwriters Insurance Company, Newmarket
                        Underwriters Insurance Company and, as the case may be,
                        AI Risk Specialists of Missouri, Inc., Eastern Risk
                        Specialists, Inc., Florida Risk Specialists, Inc.,
                        Louisiana Risk Specialists, Inc., Michigan Risk
                        Specialists, Inc., Midwestern Risk Specialists, Inc.,
                        Nevada Risk Specialists, Inc., New England Risks
                        Specialists, Inc., Northwestern Risk Specialists, Inc.,
                        Risk Specialists Companies of Colorado, Inc., Risk
                        Specialist Company of Minnesota, Inc., Risk Specialist
                        Company of New Jersey, Inc., Risk Specialist Company of
                        New York, Inc., Risk Specialist Company of Ohio, Inc.,
                        Southeastern Risk Specialist, Inc., Southern Risk
                        Specialist, Inc., and Western Risks Specialists, Inc.,
                        as amended; and

                  (ii)  Pro Rata Semi-Automatic Facultative Reinsurance
                        Agreement by and between Allied World Assurance Company
                        (U.S.), Inc. f/k/a Commercial Underwriters Insurance
                        Company, Newmarket Underwriters Insurance Company and
                        Lexington Insurance Company, American Home Assurance
                        Company of Canada (a branch of American Home Assurance
                        Company) and Commerce & Industry Insurance Company of
                        Canada.

            (c)   Section 5.6 is revised to delete the "." at the end of the
                  sentence and insert the following phrase in its place:

                  , other than the Permitted Terminations.

                                     - 2 -
<PAGE>
      3.1.2 All references in the Security Agreement to "Credit Agreement" shall
            be deemed to be references to "Credit Agreement, as amended or
            otherwise modified from time to time".

4.    CONTINUITY AND FURTHER ASSURANCE

4.1   CONTINUING OBLIGATIONS

      The provisions of the Original Credit Agreement and the Security Agreement
      shall, save as amended in this Agreement, continue in full force and
      effect.

4.2   FURTHER ASSURANCE

      The Borrower shall, at the reasonable request of the Issuer and at its own
      expense, do all such acts and such things necessary or desirable to give
      effect to the amendments effected or to be effected pursuant to this
      Agreement.

5.    CONDITIONS AND CONFIRMATIONS

5.1   CONDITIONS PRECEDENT

      This Agreement shall not become effective until the day the Issuer
      confirms to the Borrower that it has received, in form and substance
      satisfactory to it, each of the documents set out in Schedule 2
      (Conditions Precedent) (the "EFFECTIVE DATE").

5.2   SECURITY INTEREST CONFIRMATION

      5.2.1 The Borrower hereby confirms that the security interest granted to
            the Issuer under the Security Agreement shall continue to apply to
            the Amended Agreement.

6.    FEES, COSTS AND EXPENSES

6.1   EXTENSION FEE

      The Borrower shall pay to the Issuer an extension fee of $15,000 (the
      "EXTENSION FEE"), to be paid on signing of this Agreement.

6.2   TRANSACTION EXPENSES

      The Borrower shall promptly on demand pay the Issuer the amount of all
      costs and expenses (including legal fees) reasonably incurred by the
      Issuer (up to $10,000) in connection with the negotiation, preparation,
      printing and execution of this Agreement and any other documents referred
      to in this Agreement.

6.3   ENFORCEMENT COSTS

      The Borrower shall, within three Business Days of demand, pay to the
      Issuer the amount of all costs and expenses (including legal fees)
      reasonably incurred by the Issuer in connection with the enforcement of,
      or the preservation of any rights under this Agreement.

6.4   STAMP TAXES

      The Borrower shall pay and, within three Business Days of demand,
      indemnify the Issuer against any cost, loss or liability that the Issuer
      incurs in relation to all stamp duty, registration and other similar Taxes
      payable in respect of this Agreement.

                                     - 3 -
<PAGE>
7.    MISCELLANEOUS

7.1   INCORPORATION OF TERMS

      Clauses 9.4 (Entire Agreement), 9.7 (Severability of Provisions), 9.9
      (Choice of Law), 9.10 (Consent to Jurisdiction), 9.11 (Waiver of July
      Trial) and 9.12 (Counterparts) of the Original Credit Agreement shall be
      incorporated into this Agreement as if set out in full in this Agreement
      and as if references in those clauses to "this Agreement" are references
      to this Agreement.

7.2   COUNTERPARTS

      This Agreement may be executed in any number of counterparts, and this has
      the same effect as if the signatures on the counterparts were on a single
      copy of this Agreement.

      THIS AGREEMENT is effective as of the Effective Date.

                                     - 4 -
<PAGE>
SIGNATURES

ALLIED WORLD ASSURANCE COMPANY, LTD.
AS BORROWER

By: /s/ Joan H. Dillard
    ---------------------------------------------
Name:   Joan H. Dillard
Title:  Vice President & Chief Accounting Officer

BARCLAYS BANK PLC
AS ISSUER

By: /s/ R. Merchant
    ---------------------------------------------
Name:   R. Merchant
Title:  Relationship Director

                                     - 5 -<PAGE>

                                                                   EXHIBIT 10.35

THIS AGREEMENT (the "AGREEMENT") is made as of 31 December 2005 among:

(1)   ALLIED WORLD ASSURANCE COMPANY, LTD, a corporation organized under the
      laws of Bermuda, as Borrower (the "BORROWER"); and

(2)   BARCLAYS BANK PLC, as Issuer (the "ISSUER").

(A)   WHEREAS, pursuant to a letter of credit issuance facility agreement dated
      as of 31 December 2003 as amended by a Global Amendment Agreement dated as
      of January 11, 2005, each between the Borrower and the Issuer (as amended,
      increased or otherwise modified from time to time, the "ORIGINAL CREDIT
      AGREEMENT"), the Issuer issued certain letters of credit in accordance
      with the terms of the Original Credit Agreement.

(B)   WHEREAS, pursuant to a Security Agreement dated as of 31 December 2003 (as
      amended or otherwise modified from time to time, the "SECURITY AGREEMENT")
      executed by the Borrower in favor of the Issuer, the Borrower granted a
      security interest in the Collateral (as defined therein) to the Issuer.

(C)   WHEREAS the parties desire to extend the tenure of the Credit Agreement
      and make certain other amendments to the documents described above, all as
      set out below.

IT IS AGREED as follows:

1.    DEFINITIONS AND INTERPRETATION

1.1   DEFINITIONS

      In this Agreement:

      "AMENDED AGREEMENT" means the Original Credit Agreement as amended by this
      Agreement.

      "EFFECTIVE DATE" shall have the meaning given to it in Clause 5.1.

1.2   INCORPORATION OF DEFINED TERMS

      Terms not otherwise defined in this Agreement shall have the same meaning
      as set forth in the Original Credit Agreement.

1.3   CLAUSES

      (a)   In this Agreement any reference to a "Clause" or "Schedule" is,
            unless the context otherwise requires, a reference to a Clause or
            Schedule of this Agreement.

      (b)   Clause and Schedule headings are for ease of reference only.

2.    REPRESENTATIONS

      The Borrower repeats the representations set out in Clause 5
      (Representations and Warranties) of the Original Credit Agreement as
      amended by Clause 3 below as if

                                      -1-
<PAGE>

      each reference in those representations to "this Agreement" includes a
      reference to (a) this Agreement and (b) the Amended Agreement.

3.    AMENDMENTS

3.1   AMENDMENT OF THE ORIGINAL CREDIT AGREEMENT

      With effect from the Effective Date the Original Credit Agreement shall be
      amended as follows:

      3.1.1 In clause (A) of the Recitals the term "$125,000,000" shall be
            deleted and replaced with the term "$250,000,000."

      3.1.2 In the definition of "AGGREGATE FACILITY LC COMMITMENT" the term
            "$125,000,000" shall be deleted and replaced with the term
            "$250,000,000."

      3.1.3 The definition of "COLLATERAL" shall be deleted in its entirety and
            replaced with:

                  "COLLATERAL" means at any time US Government Securities.

      3.1.4 The definition of "US GOVERNMENT SECURITIES" shall be deleted in its
            entirety and replaced with:

                  "US GOVERNMENT SECURITIES" means at any time treasury bills,
                  notes and bonds issued by the US Government (but excluding
                  securities issued by any agency of the US Government) and
                  which are rated at least AAA by S&P and which have a remaining
                  modified duration of less than eight years.

      3.1.5 The definition of "LC FACILITY TERMINATION DATE" shall be deleted in
            its entirety and replaced with:

                  "LC FACILITY TERMINATION DATE" means December 31, 2008 (as
                  such date may be extended by amendment hereto) or any earlier
                  date on which the Aggregate Facility LC Commitment is reduced
                  to zero or otherwise terminated and/or the Facility LC
                  Obligations shall become due and payable in accordance with
                  the provisions of this Agreement.

      3.1.6 The following definitions shall be added to Clause 1 (Definitions):

            (a)   "AWAH FACILITY" means (i) the Credit Agreement dated as of
                  March 30, 2005 among the Parent, Bank of America N.A.,
                  Wachovia Bank, National Association and the other lenders
                  party thereto, as amended, modified or supplemented from time
                  to time and (ii) any loan agreement, credit agreement or
                  similar agreement entered into in replacement or refinancing
                  thereof.

            (b)   "PARENT" means Allied World Assurance Holdings, Ltd, an
                  exempted Bermuda company.

                                      -2-
<PAGE>

      3.1.7 Clause 5.6 shall be deleted in its entirety and replaced with the
            following:

            Since 31 December 2003, there has been no change in the business,
            Property, condition (financial or otherwise), prospects or results
            of operations of the Borrower and its Subsidiaries taken as a whole
            which could reasonably be expected to have a Material Adverse Effect
            except (i) for the cumulative effects of hurricanes Katrina, Rita
            and Wilma during the 2005 hurricane season of the United States of
            America, (ii) as described in Clause 5.8 (Litigation and Contingent
            Obligations) and (iii) the Permitted Terminations.

      3.1.8 Clause 5.8 shall be deleted in its entirety and replaced with the
            following:

            There is no litigation, arbitration, governmental investigation,
            proceeding or inquiry pending or, to the knowledge of any of their
            officers, threatened against or affecting the Borrower or any of its
            Subsidiaries which could reasonably be expected to (a) have a
            Material Adverse Effect except for the investigation by the Attorney
            General of the State of Texas into price fixing and/or bid-rigging
            by the Borrower and anti-competitive behaviour involving the
            Borrower or (b) prevent, enjoin or unduly delay the issuance of
            Facility LCs under this Agreement. As of the date hereof, the
            Borrower has no material Contingent Obligations not provided for or
            disclosed in the Financial Statements.

      3.1.9 A new Clause 7.12 shall be added as follows:

            7.12  The occurrence of an Event of Default (as defined in the AWAH
                  Facility) under the AWAH Facility.

4.    CONTINUITY AND FURTHER ASSURANCE

4.1   CONTINUING OBLIGATIONS

      The provisions of the Original Credit Agreement and the Security Agreement
      shall, save as amended in this Agreement, continue in full force and
      effect.

4.2   FURTHER ASSURANCE

      The Borrower shall, at the reasonable request of the Issuer and at its own
      expense, do all such acts and such things necessary or desirable to give
      effect to the amendments effected or to be effected pursuant to this
      Agreement.

5.    EFFECTIVENESS AND CONFIRMATION

5.1   EFFECTIVENESS

      This Agreement shall become effective as of 31 December 2005 upon
      confirmation by the Issuer to the Borrower that the Issuer has received,
      in form and substance satisfactory to it, each of the documents set out in
      Schedule 1 (Conditions Precedent) (the "EFFECTIVE DATE").

5.2   SECURITY INTEREST CONFIRMATION

                                      -3-
<PAGE>

      The Borrower hereby confirms that the security interest granted to the
      Issuer under the Security Agreement shall continue to apply to the Amended
      Agreement.

6.    FEES, COSTS AND EXPENSES

6.1   EXTENSION FEE

      The Borrower shall pay to the Issuer an extension fee of $85,000 (the
      "EXTENSION FEE"), to be paid on signing of this Agreement.

6.2   TRANSACTION EXPENSES

      The Borrower shall promptly on demand pay the Issuer the amount of all
      costs and expenses (including legal fees) reasonably incurred by the
      Issuer in connection with the negotiation, preparation, printing and
      execution of this Agreement and any other documents referred to in this
      Agreement.

6.3   ENFORCEMENT COSTS

      The Borrower shall, within three Business Days of demand, pay to the
      Issuer the amount of all costs and expenses (including legal fees)
      reasonably incurred by the Issuer in connection with the enforcement of,
      or the preservation of any rights under this Agreement.

6.4   STAMP TAXES

      The Borrower shall pay and, within three Business Days of demand,
      indemnify the Issuer against any cost, loss or liability that the Issuer
      incurs in relation to all stamp duty, registration and other similar Taxes
      payable in respect of this Agreement.

7.    MISCELLANEOUS

7.1   INCORPORATION OF TERMS

      Clauses 9.4 (Entire Agreement), 9.7 (Severability of Provisions), 9.9
      (Choice of Law), 9.10 (Consent to Jurisdiction), 9.11 (Waiver of Jury
      Trial) and 9.12 (Counterparts) of the Original Credit Agreement shall be
      incorporated into this Agreement as if set out in full in this Agreement
      and as if references in those clauses to "this Agreement" are references
      to this Agreement.

7.2   COUNTERPARTS

      This Agreement may be executed in any number of counterparts, and this has
      the same effect as if the signatures on the counterparts were on a single
      copy of this Agreement.

      THIS AGREEMENT is effective as of the Effective Date.

                                      -4-
<PAGE>

SIGNATURES

ALLIED WORLD ASSURANCE COMPANY, LTD
AS BORROWER

By: /s/ Joan H. Dillard
    ----------------------
Name: Joan H. Dillard

Title: Senior Vice President & Chief Financial Officer

By: /s/ Marchelle D. Lewis
    ----------------------
Name: Marchelle D. Lewis

Title: Vice President & Treasurer

BARCLAYS BANK PLC
AS ISSUER

By:  /s/ Jonathan Wright
   ------------------------------------
Name:  Jonathan Wright
     ----------------------------------
Title:  Corporate Credit Analyst
       --------------------------------

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