These definitive additional materials (the “Definitive Additional Materials”) amend and supplement the definitive proxy statement, dated October 14, 2026 (the “definitive proxy statement”), initially mailed on or about October 14, 2026, by Bowhead Specialty Holdings Inc., a Delaware corporation (“Bowhead” or the “Company,” “we,” “our” or “us”) to stockholders of the Company (“stockholders”) relating to a special meeting (the “special meeting”) of the stockholders, which will be held on November 13, 2026 commencing at 9:00 a.m. (Eastern time), or at any adjournment or postponement thereof, in a virtual meeting format only.

At the special meeting, holders of shares of common stock of the Company (“common shares”), par value $0.01 per common share, will be asked to consider and vote on the proposal to adopt the Agreement and Plan of Merger, dated as of August 2, 2026 (as amended, supplemented or otherwise modified from time to time, the “Merger Agreement”), by and among American Family Mutual Insurance Company, S.I., a Wisconsin insurance company (“Parent”), Trident Superior Inc., a Delaware corporation and wholly-owned direct subsidiary of Parent (“Merger Sub”), and the Company and approve the transactions contemplated by the Merger Agreement, including the merger. Pursuant to the Merger Agreement, at the effective time of the merger, Merger Sub will be merged with and into the Company, the separate corporate existence of Merger Sub will cease and the Company will continue its corporate existence under the General Corporation Law of the State of Delaware as the surviving corporation in the merger. Parent will own 100% of the shares of common stock of the Company (as the surviving corporation in the merger) following the transactions contemplated by the Merger Agreement.

These Definitive Additional Materials have been filed by the Company with the United States Securities and Exchange Commission (the “SEC”) on November 3, 2026.

If any stockholders have not already submitted a proxy for use at the special meeting, they are urged to do so promptly. No action in connection with this supplement is required by any stockholder who has previously delivered a proxy and who does not wish to revoke or change that proxy.

If any stockholders have more questions about the merger or how to submit their proxies or if any stockholders need additional copies of the definitive proxy statement, this supplement, the proxy card or voting instructions, please contact the Company’s proxy solicitor:

The information contained herein speaks only as of November 3, 2026, unless the information specifically indicates that another date applies.

This supplemental information should be read in conjunction with the definitive proxy statement, which should each be read in their entirety. The Company believes that no further disclosure is required to supplement the definitive proxy statement under applicable law; however, to avoid the risks and uncertainties inherent in litigation and the risk that lawsuits may delay or otherwise adversely affect the consummation of the proposed merger and to minimize the expense of defending such actions, the Company wishes to make supplemental disclosures related to the proposed merger, which are set forth below, in response to certain allegations. Nothing in these supplemental disclosures shall be deemed an admission of liability or the legal necessity or materiality under applicable law of any of the disclosures set forth herein. To the extent that information in these Definitive Additional Materials differs from or conflicts with information contained in the definitive proxy statement, the information in these Definitive Additional Materials shall supersede or supplement the information in the definitive proxy statement, as applicable. Defined terms used but not defined herein have the meanings set forth in the definitive proxy statement.

The disclosure under the section entitled “SPECIAL FACTORS” in the definitive proxy statement is hereby amended and supplemented by adding the following bolded and double underlined language in the eighth paragraph on page 24 of the definitive proxy statement under the section heading entitled “Background of the Merger”:

On June 8, 2026, the Company and Party B entered into a confidentiality agreement containing customary terms, including a standstill provision that fell away upon the execution of the Merger Agreement. Neither the confidentiality agreement by and between the Company and American Family, nor the confidentiality agreement by and between the Company and Party B, contained “don’t ask, don’t waive” provisions.

The disclosure under the section entitled “SPECIAL FACTORS” in the definitive proxy statement is hereby amended and supplemented by adding the following bolded and double underlined paragraph immediately after the first paragraph on page 31 of the definitive proxy statement under the section heading entitled “Background of the Merger”:

Also on July 30, 2026, representatives of the Company’s management then reviewed with the Board the updated business plan (including projections) for the Company reflecting the new ceded reinsurance program that became effective May 1, 2026. The Board adopted the updated business plan on July 30, 2026.

The disclosure under the section entitled “SPECIAL FACTORS” in the definitive proxy statement is hereby amended and supplemented by adding the following bolded and double underlined language in the table on page 39 of the definitive proxy statement under the section heading entitled “2. Selected Companies Analysis”:

The disclosure under the section entitled “SPECIAL FACTORS” in the definitive proxy statement is hereby amended and supplemented by adding the following bolded and double underlined language in the fifth paragraph on page 39 of the definitive proxy statement under the section heading entitled “Opinion of Ardea”:

Based on the results of the foregoing calculations and Ardea’s professional judgment and experience, Ardea applied a reference range of (i) P/2026E EPS multiples of 11.1x to 21.1x to the Company’s 2026 estimated earnings per common share based on the Forecasts (being $2.30), resulting in an illustrative range of implied equity values per common share of $25.58 to $48.57 per common share and (ii) P/2027E EPS multiples of 9.5x to 22.6x to the Company’s 2027 estimated earnings per common share based on the Forecasts (being $2.75), resulting in an illustrative range of implied values of $26.19 to $62.14 per common share.

The disclosure under the section entitled “SPECIAL FACTORS” in the definitive proxy statement is hereby amended and supplemented by adding the following bolded and double underlined language in the last paragraph on page 40 of the definitive proxy statement under the section heading entitled “Opinion of Ardea”:

Ardea served as financial advisor to Gallatin Point in connection with a strategic partnership with Capital Constellation, an investment platform managed by Wafra Inc., for which Ardea was paid a fee, in February 2026, of $2,250,000 by Gallatin Point.

The disclosure under the section entitled “IMPORTANT INFORMATION REGARDING THE COMPANY” in the definitive proxy statement is hereby amended and supplemented by adding the following bolded and double underlined language on page 112 of the definitive proxy statement under the section heading entitled “Legal Proceedings”:

The Company is subject to routine legal proceedings in the normal course of operating an insurance business. The Company is not currently a party to any such claims, lawsuits or proceedings, the outcome of which, if determined adversely, would, individually or in the aggregate, have a material adverse effect on the business, results of operations or financial condition.

These Definitive Additional Materials and the definitive proxy statement, and the documents incorporated by reference in this proxy statement, and any related oral statements, contain “forward-looking statements” that do not directly or exclusively relate to historical facts, including, without limitation, statements relating to the Merger Agreement, the merger and the other transactions contemplated by the Merger Agreement. Some of the forward-looking statements can be identified by the use of terms such as “believes,” “expects,” “may,” “will,” “should,” “could,” “seeks,” “intends,” “plans,” “estimates,” “anticipates” or other comparable terms or the converse of such terms. However, not all forward-looking statements contain these identifying words. These forward-looking statements include all matters that are not related to present facts or current conditions or that are not historical facts. They appear in a number of places throughout these Definitive Additional Materials and the definitive proxy statement and the documents incorporated by reference in these Definitive Additional Materials and the definitive proxy statement and include statements regarding intentions, beliefs or current expectations concerning, among other things, the merger, regulatory approvals, and the timing of the merger, the industries in which the Company operates, and other statements relating to the Company’s future performance.

The merger is subject to risks and uncertainties, including:

• that the Company and Parent may be unable to complete the merger because, among other reasons, conditions to the closing of the merger, as detailed in the section titled “The Merger Agreement — Conditions to the Merger” beginning on page 96 of the definitive proxy statement, may not be satisfied or waived;

•  uncertainty as to the timing of the closing of the merger;

•  the inability to complete the merger due to the failure to obtain the requisite approval of the stockholders or the failure to satisfy other conditions to the closing of the merger, including that a governmental entity may prohibit, delay or refuse to grant approval for the consummation of the merger;

•  interloper risk;

•  the occurrence of any event, change or other circumstances that could give rise to the termination of the Merger Agreement;

•  risks related to disruption of management’s attention from the Company’s ongoing business operations due to the merger;

•  the effect of the announcement of the merger on the Company’s relationships with its insureds, operating results and business generally; and

•  the outcome of any legal proceedings to the extent initiated against the Company, Parent or others following the announcement of the merger, as well as the Company’s and Parent’s management’s response to any of the aforementioned factors.

For a discussion of factors that could cause actual results to differ materially from those contemplated by forward-looking statements, see the section captioned “Risk Factors” in the Company’s Annual Report on Form 10-K for the fiscal year ended December 31, 2025, subsequent Quarterly Reports on Form 10-Q and other filings with the SEC. See the section of these Definitive Additional Materials below titled “Where You Can Find Additional Information.”

Should one (1) or more of these risks or uncertainties materialize, or should underlying assumptions prove incorrect, actual results may vary materially from those indicated or anticipated by such forward-looking statements. While the list of factors presented here is considered representative, no such list should be considered to be a complete statement of all potential risks and uncertainties. Unlisted factors may present significant additional obstacles to the realization of forward-looking statements.

Forward-looking statements speak only as of the date on which they are made. Except as expressly required under federal securities laws or the rules and regulations of the SEC, the Company does not assume any obligation to update or revise any forward-looking statement, whether as a result of new information, future events or otherwise. You should not place undue reliance on forward-looking statements. All forward-looking statements attributable to the Company are expressly qualified by these cautionary statements.

We file annual, quarterly and current reports, proxy statements and other information with the SEC. Our SEC filings are available to the public on the SEC’s website at http://www.sec.gov. We will provide, without charge, to each person, including any beneficial owner, to whom a copy of these Definitive Additional Materials or the definitive proxy statement are delivered, upon written or oral request of such person, a copy of any or all of the reports and documents referred to above which have been or may be incorporated by reference into these Definitive Additional Materials or the definitive proxy statement. You should direct requests for those documents to Investor Relations, Bowhead Specialty Holdings Inc., 452 Fifth Avenue, 24th Floor, New York, New York 10018, Telephone: (212) 970-0269, Email: investorrelations@bowheadspecialty.com. Our reports and documents incorporated by reference herein may also be found in the “Investors” section of our website at https://www.bowheadspecialty.com. Except as expressly set forth below, we are not incorporating by reference the contents of the SEC website or our website into these Definitive Additional Materials or the definitive proxy statement.

Because the merger is a “going-private” transaction, Parent, the Company and Merger Sub have filed with the SEC a Transaction Statement on Schedule 13e-3 with respect to the merger. The Schedule 13e-3, including any amendments and exhibits filed or incorporated by reference as a part of it, is available for inspection as set forth above. The Schedule 13e-3 will be amended to report promptly any material change in the information set forth in the most recent Schedule 13e-3 filed with the SEC.

The SEC allows us to incorporate by reference the information we file with the SEC, which means that we can disclose important information to you by referring you to those documents. The information that we incorporate by reference is considered to be part of these Definitive Additional Materials or the definitive proxy statement and with respect to these Definitive Additional Materials or the definitive proxy statement but not with respect to the Schedule 13e-3, later information that we file later with the SEC will automatically update and supersede information in these Definitive Additional Materials or the definitive proxy statement or in any documents previously incorporated by reference. This means that you must look at all of the SEC filings that we incorporate by reference to determine if any of the statements in these Definitive Additional Materials or the definitive proxy statement, or in any documents previously incorporated by reference, have been modified or superseded. Information in documents that is deemed, in accordance with SEC rules, to be furnished and not filed is not deemed to be incorporated by reference into these Definitive Additional Materials or the definitive proxy statement. We incorporate by reference the documents listed below and, with respect to these Definitive Additional Materials or the definitive proxy statement, but not with respect to the Schedule 13e-3, any documents filed by us pursuant to Section 13(a), 13(c), 14 or 15(d) of the Exchange Act after the date of these Definitive Additional Materials and prior to the date of the special meeting:

•  our Annual Report on Form 10-K for the fiscal year ended December 31, 2025, filed with the SEC on February 24, 2026;

•  portions of our definitive proxy statement on Schedule 14A, filed with the SEC on March 16, 2026, that are incorporated by reference into Part III of our Annual Report on Form 10-K for the year ended December 31, 2025;

•  our Quarterly Reports on Form 10-Q for the quarterly periods ended March 31, 2026, June 30, 2026, and September 30, 2026, filed with the SEC on May 5, 2026, August 3, 2026, and November 3, 2026 respectively;

•  our Current Reports on Form 8-K filed on May 5, 2026, August 3, 2026, August 19, 2026 September 14, 2026 and November 3, 2026; and

•  our definitive proxy statement on Schedule 14A, filed with the SEC on October 14, 2026.

We are not incorporating by reference any information furnished under Items 2.02 or 7.01 (or corresponding information furnished under Item 9.01 or included as an exhibit) in any past or future Current Reports on Form 8-K that we may file with the SEC, unless otherwise specified in such Current Report.

We will amend the Schedule 13e-3 to incorporate by reference any additional documents that we may file with the SEC under Section 13(a), 13(c), 14 or 15(d) of the Exchange Act after the date of these Definitive Additional Materials and prior to the date of the special meeting to the extent required to fulfill our obligations under the Exchange Act.

No persons have been authorized to give any information or to make any representations other than those contained in these Definitive Additional Materials and the definitive proxy statement and, if given or made, such information or representations must not be relied upon as having been authorized by us or any other person. These Definitive Additional Materials are dated as of November 3, 2026. You should not assume that the information contained in these Definitive Additional Materials is accurate as of any date other than that date, and any mailing of these Definitive Additional Materials to stockholders will not create any implication to the contrary.

The Company has supplied all information relating to the Company, and Parent has supplied, and the Company has not independently verified, all of the information relating to KBW, Parent and Merger Sub contained in these Definitive Additional Materials and the definitive proxy statement.

YOU SHOULD RELY ONLY ON THE INFORMATION CONTAINED OR INCORPORATED BY REFERENCE IN THESE DEFINITIVE ADDITIONAL MATERIALS AND THE DEFINITIVE PROXY STATEMENT IN VOTING YOUR COMMON SHARES AT THE SPECIAL MEETING. THE COMPANY HAS NOT AUTHORIZED ANYONE TO PROVIDE YOU WITH INFORMATION THAT IS DIFFERENT FROM WHAT IS CONTAINED IN THESE DEFINITIVE ADDITIONAL MATERIALS OR THE DEFINITIVE PROXY STATEMENT. THESE DEFINITIVE ADDITIONAL MATERIALS ARE DATED NOVEMBER 3, 2026. YOU SHOULD NOT ASSUME THAT THE INFORMATION CONTAINED IN THESE DEFINITIVE ADDITIONAL MATERIALS IS ACCURATE AS OF ANY DATE OTHER THAN THAT DATE (OR AS OF AN EARLIER DATE IF SO INDICATED IN THESE DEFINITIVE ADDITIONAL MATERIALS), AND THE SENDING OF THESE DEFINITIVE ADDITIONAL MATERIALS TO STOCKHOLDERS DOES NOT CREATE ANY IMPLICATION TO THE CONTRARY. THESE DEFINITIVE ADDITIONAL MATERIALS DO NOT CONSTITUTE A SOLICITATION OF A PROXY IN ANY JURISDICTION WHERE, OR TO OR FROM ANY PERSON TO WHOM, IT IS UNLAWFUL TO MAKE A PROXY SOLICITATION.