UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

SCHEDULE 14A

Proxy Statement Pursuant to Section 14(a) of the

Securities Exchange Act of 1934

Filed by the Registrant  ¨                            Filed by a Party other than the Registrant  x

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¨ Preliminary Proxy Statement

¨ Confidential, for Use of the Commission Only (as permitted by Rule 14a-6(e)(2))

¨ Definitive Proxy Statement

x Definitive Additional Materials

¨ Soliciting Material under §240.14a–12

ASPEN INSURANCE HOLDINGS LIMITED

(Name of Registrant as Specified In Its Charter)

ENDURANCE SPECIALTY HOLDINGS LTD.

(Name of Person(s) Filing Proxy Statement if other than the Registrant)

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PEMBROKE, Bermuda, July 1, 2014 – In response to the Aspen letter issued today, an Endurance spokesperson stated:

“The ongoing rhetoric contained in Aspen’s letter about governance and compensation is a continuation of their efforts to deliberately distract Aspen’s shareholders from our proposed transaction – which provides a highly attractive premium and compelling value – in an attempt to prevent Aspen shareholders from having their voices heard. Noticeably absent from Aspen’s letter is any discussion of their long track record of poor operating performance under current management and dismal corporate governance practices.

“Aspen’s statements regarding John Charman’s compensation arrangements are clearly misleading. The facts are clear: no other CEO in our industry is aligned with shareholders like John Charman. He invested $30 million of his own capital in Endurance upon joining the company, committed to invest an additional $25 million in connection with the Aspen transaction and receives no base salary or other compensation, all of which is evidence that he is fully committed to the company as a shareholder on a long-term basis.

“We are confident that Aspen shareholders – who have overwhelmingly indicated their support for the transaction – will see through this smokescreen and vote to send a clear message to the Aspen Board that now is the time to engage with Endurance and to take concrete action towards realizing the compelling value of the transaction.”

Additional Information about the Proposed Transaction and Where to Find It

This communication relates to the offer commenced by Endurance to exchange each issued and outstanding common share of Aspen (together with associated preferred share purchase rights) for $49.50 in cash, 0.9197 Endurance common shares, or a combination of cash and Endurance common shares, subject to a customary proration mechanism. This communication is for informational purposes only and does not constitute an offer to exchange, or a solicitation of an offer to exchange, Aspen common shares, nor is it a substitute for the Tender Offer Statement on Schedule TO or the Prospectus/Offer to Exchange included in the Registration Statement on Form S-4 (including the Letter of Election and Transmittal and related documents and as amended from time to time, the “Exchange Offer Documents”) that Endurance has filed with the SEC. The Endurance exchange offer will be made only through the Exchange Offer Documents.

This communication is not a substitute for any other relevant documents that Endurance may file with the SEC or any other documents that Endurance may send to its or Aspen’s shareholders in connection with the proposed transaction. Endurance has sent to Aspen shareholders a solicitation statement with respect to the solicitation of (i) written requisitions that the board of directors of Aspen convene a special general meeting of Aspen’s shareholders to vote on an increase in the size of Aspen’s board of directors from 12 to 19 directors and (ii) Aspen shareholder support for the proposal of a scheme of arrangement by Endurance which will entail the holding of a court-ordered meeting of Aspen shareholders at which Aspen’s shareholders would vote to approve a scheme of arrangement under Bermuda law pursuant to which Endurance would acquire all of Aspen’s outstanding common shares on financial terms no less favorable than those contained in its acquisition proposal announced on June 2, 2014 (the “Solicitation Statement”).

INVESTORS AND SECURITY HOLDERS ARE URGED TO READ THE EXCHANGE OFFER DOCUMENTS AND THE SOLICITATION STATEMENT AND ANY OTHER RELEVANT DOCUMENTS THAT ENDURANCE HAS FILED OR MAY FILE WITH THE SEC IF AND WHEN THEY BECOME AVAILABLE BECAUSE THEY CONTAIN OR WILL CONTAIN IMPORTANT INFORMATION ABOUT THE PROPOSED TRANSACTION. All such documents, when filed, are available free of charge at the SEC’s website (www.sec.gov) or by directing a request to Endurance at the Investor Relations contact below.

Participants in the Solicitation

Endurance and its directors and certain of its executive officers and employees may be deemed to be participants in any solicitation of shareholders in connection with the proposed transaction. Information about Endurance’s directors, executive officers and employees who may be deemed to be participants in the solicitation, including a description of their direct and indirect interests, by security holdings or otherwise, is set forth in the Solicitation Statement and Endurance’s proxy statement, dated April 9, 2014, for its 2014 annual general meeting of shareholders.

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