Exhibit 10.37

SUPPLEMENTAL CONFIRMATION

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[spacer.gif] [spacer.gif] [spacer.gif] [spacer.gif] To: [spacer.gif]
[spacer.gif] Aspen Insurance Holdings Limited
Maxwell Roberts Building
1 Church Street
Hamilton, HM 11
Bermuda From: [spacer.gif] [spacer.gif] Goldman, Sachs & Co. Subject:
[spacer.gif] [spacer.gif] Collared Accelerated Stock Buyback Ref. No:
[spacer.gif] [spacer.gif] [Insert Reference No.] Date: [spacer.gif] [spacer.gif]
December 21, 2006 [spacer.gif]

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The purpose of this Supplemental Confirmation is to confirm the terms and
conditions of the Transaction entered into between Goldman, Sachs & Co.
(‘‘GS&Co.’’) and Aspen Insurance Holdings Limited (‘‘Counterparty’’) (together,
the ‘‘Contracting Parties’’) on the Trade Date specified below. This
Supplemental Confirmation is a binding contract between GS&Co. and Counterparty
as of the relevant Trade Date for the Transaction referenced below.

1.    This Supplemental Confirmation supplements, forms part of, and is subject
to the Master Confirmation dated as of December 21, 2006 (the ‘‘Master
Confirmation’’) between the Contracting Parties, as amended and supplemented
from time to time. All provisions contained in the Master Confirmation govern
this Supplemental Confirmation except as expressly modified below.

2.    The terms of the Transaction to which this Supplemental Confirmation
relates are as follows:

[spacer.gif] [spacer.gif] [spacer.gif] Trade Date: [spacer.gif] December 21,
2006

[spacer.gif] [spacer.gif] [spacer.gif] Forward Price Adjustment Amount:
[spacer.gif] USD0.18

[spacer.gif] [spacer.gif] [spacer.gif] Hedge Completion Date: [spacer.gif] As
set forth in the Trade Notification, but in no event later than January 19,
2007.

[spacer.gif] [spacer.gif] [spacer.gif] Scheduled Termination Date: [spacer.gif]
Three months after the Hedge Completion Date, subject to GS&Co.’s right to
accelerate the Termination Date to any date on or after the First Acceleration
Date.

[spacer.gif] [spacer.gif] [spacer.gif] First Acceleration Date: [spacer.gif] As
set forth in the Trade Notification to be the date that follows the Hedge
Completion Date by one month.

[spacer.gif] [spacer.gif] [spacer.gif] Prepayment Amount: [spacer.gif]
USD44,000,000.00

[spacer.gif] [spacer.gif] [spacer.gif] Minimum Shares: [spacer.gif] As set forth
in the Trade Notification, to be a number of Shares equal to (a) the Prepayment
Amount divided by (b) 107% of the Hedge Period Reference Price.

[spacer.gif] [spacer.gif] [spacer.gif] Maximum Shares: [spacer.gif] As set for
in the Trade Notification, to be a number of Shares equal to (a) the Prepayment
Amount divided by (b) 98% of the Hedge Period Reference Price.

[spacer.gif] [spacer.gif] [spacer.gif] Ordinary Dividend Amount: [spacer.gif]
For any calendar quarter, USD0.15

3.    Counterparty represents and warrants to GS&Co. that neither it nor any
‘‘affiliated purchaser’’ (as defined in Rule 10b-18 under the Exchange Act) has
made any purchases of blocks pursuant to the proviso in Rule 10b-18(b)(4) under
the Exchange Act during the four full calendar weeks immediately preceding the
Trade Date.

4.    This Supplemental Confirmation may be executed in any number of
counterparts, all of which shall constitute one and the same instrument, and any
party hereto may execute this Supplemental Confirmation by signing and
delivering one or more counterparts.

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Counterparty hereby agrees (a) to check this Supplemental Confirmation carefully
and immediately upon receipt so that errors or discrepancies can be promptly
identified and rectified and (b) to confirm that the foregoing (in the exact
form provided by GS&Co.) correctly sets forth the terms of the agreement between
GS&Co. and Counterparty with respect to this Transaction, by manually signing
this Supplemental Confirmation or this page hereof as evidence of agreement to
such terms and providing the other information requested herein and immediately
returning an executed copy to Equity Derivatives Documentation Department,
Facsimile No. 212-428-1980/83.

[spacer.gif] Yours sincerely,

[spacer.gif] GOLDMAN, SACHS & CO.

[spacer.gif] By:/s/ David Goldenberg                        
                    Authorized Signatory

Agreed and accepted by:

ASPEN INSURANCE HOLDINGS LIMITED

By:  /s/ Julian Cusack                                
Name:    Julian Cusack
Title:    Chief Financial Officer

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