Common Stock Purchase Warrant

NEITHER THIS SECURITY NOR THE SECURITIES AS TO WHICH THIS SECURITY MAY BE EXERCISED HAVE BEEN REGISTERED WITH THE SECURITIES AND EXCHANGE COMMISSION OR THE SECURITIES COMMISSION OF ANY STATE IN RELIANCE UPON AN EXEMPTION FROM REGISTRATION UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE “SECURITIES ACT”), AND, ACCORDINGLY, MAY NOT BE OFFERED OR SOLD EXCEPT PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT UNDER THE SECURITIES ACT OR PURSUANT TO AN AVAILABLE EXEMPTION FROM, OR IN A TRANSACTION NOT SUBJECT TO, THE REGISTRATION REQUIREMENTS OF THE SECURITIES ACT AND IN ACCORDANCE WITH APPLICABLE STATE SECURITIES LAWS AS EVIDENCED BY A LEGAL OPINION OF COUNSEL TO THE TRANSFEROR TO SUCH EFFECT, THE SUBSTANCE OF WHICH SHALL BE REASONABLY ACCEPTABLE TO THE COMPANY.

This COMMON STOCK PURCHASE WARRANT (this “Warrant”) certifies that, for value received, American Family Mutual Insurance Company, S.I., a Wisconsin corporation (the “Holder”), is entitled, upon the terms and subject to the limitations on exercise and the conditions hereinafter set forth, to purchase from Bowhead Specialty Holdings Inc., a Delaware corporation (the “Company”), (i) up to 1,614,250 shares of Common Stock (as defined below) and (ii) if applicable, up to 56,471 additional shares of Common Stock to the extent the underwriters’ overallotment option in the initial public offering of the Company (the “Over-allotment Option”) is exercised (subject to any adjustments pursuant to Section 3 hereof, clauses (i) and (ii) collectively, the “Warrant Shares”), which represent the number of shares of Common Stock that would constitute five percent (5%) of all issued and outstanding shares of Common Stock on a Fully Diluted basis as of the Issuance Date or, if applicable, the date of the closing of the Over-allotment Option, assuming the Holder has exercised this Warrant in full on a cash basis. The purchase price of one share of Common Stock under this Warrant shall be equal to the Exercise Price (as defined in Section 2(b) hereof). Subject to Section 5 hereof, this Warrant shall vest ratably over five (5) years such that it shall become exercisable with respect to an initial twenty percent (20%) of the Warrant Shares on the first anniversary of the Issuance Date and an additional twenty percent (20%) of the Warrant Shares on each of the second, third, fourth and fifth anniversaries of the Issuance Date. Subject to Section 5(b) hereof, the vested portion may be exercised at any time, in whole or in part, until 5:00 p.m. eastern time on the ten-year anniversary of the Issuance Date (the “Exercise Period”).

1.DEFINED TERMS. For purposes of this Warrant, the following terms shall have the following meanings:

(a)“Business Day” means any day except any Saturday, any Sunday, any day which is a federal legal holiday in the United States or any day on which banking institutions in the State of New York are authorized or required by law or other governmental action to close.

(b)“Change of Control” means (a) the sale, transfer, or other disposition of all or substantially all of the Company’s assets, (b) any merger, consolidation or other business combination transaction of the Company with or into another corporation, entity or person, other than a transaction in which the holders of at least a majority of the shares of voting capital stock of the Company outstanding immediately prior to such transaction continue to hold (either by such shares remaining outstanding or by their being converted into shares of voting capital stock of the surviving entity) a majority of the total voting power represented by the shares of voting capital stock of the Company (or the surviving entity) outstanding immediately after such transaction, or (c) the direct or indirect acquisition (including by way of a tender or exchange offer) by any person or persons acting as a group (other than by GPC Partners Investments (SPV III) LP or its affiliates (including any fund controlled by GPC Partners Investments (SPV III) LP or its affiliates)) of beneficial ownership or a right to acquire beneficial ownership of shares representing a majority of the voting power of the then outstanding shares of capital stock of the Company. A Change of Control shall not include (i) the Reorganization Transaction or (ii) a transaction if its sole purpose is to change the state of the Company’s incorporation or to create a holding company that will be owned in substantially the same proportions by the persons who held the Company’s securities immediately before such

(c)“Closing Sale Price” means, for any security as of any date, (i) the last closing trade price for such security on the Principal Market or, if the Principal Market begins to operate on an extended hours basis and does not designate the closing trade price, then the last trade price of such security prior to 4:00 p.m., New York time, or (ii) if the foregoing does not apply, the last trade price of such security on the OTC for such security, or (iii) if no last trade price is reported for such security, the average of the bid and ask prices of any market makers for such security as reported by the OTC. All such determinations to be appropriately adjusted for any stock dividend, stock split, stock combination or other similar transaction during the applicable calculation period.

(d)“Common Stock” means the Company’s common stock, and any other class of securities into which such securities may hereafter be reclassified or changed.

(e)“Common Stock Equivalents” means any securities of the Company that would entitle the holder thereof to acquire at any time Common Stock, including without limitation any debt, preferred stock, rights, options, warrants or other instrument that is at any time directly or indirectly convertible into or exercisable or exchangeable for, or otherwise entitles the holder thereof to receive, with or without payment of additional consideration in cash or property, shares of Common Stock, either immediately or upon the onset of a specified date or the happening of a specified event; provided, however, in no event shall this Warrant or the Warrant Shares be considered Common Stock Equivalents.

(f)“Fair Market Value” means, as of any particular date (i) the Closing Sale Price per share of Common Stock for such date on the Principal Market on which the Common Stock is at the time listed, (ii) if there have been no sales of the Common Stock on such Principal Market on any such date, the average of the highest bid and lowest asked prices for the Common Stock on the Principal Market at the end of such date, (iii) if on any such day the Common Stock is not listed on a national securities exchange, the Closing Sale Price of the Common Stock as quoted on the OTC for such date, (iv) if there have been no sales of the Common Stock on the OTC on such date, the average of the highest bid and lowest asked prices for the Common Stock quoted on the OTC at the end of such date or (v) if at any time the Common Stock is not listed on any domestic securities exchange or quoted on the OTC, the fair market value per share as determined in good faith by the Company’s Board of Directors.

(g)“Fully Diluted” means, with respect to the Common Stock, as of a particular time the total outstanding shares of Common Stock as of such time, determined by treating all outstanding Common Stock Equivalents (regardless of whether such Common Stock Equivalents are at such time exercisable, convertible or exchangeable) as having been exercised, converted or exchanged (including the exercise, conversion or exchange of Common Stock Equivalents underlying any such Common Stock Equivalents, giving effect to any applicable caps on conversion), including any shares of Common Stock or Common Stock Equivalents issued or sold or deemed to have been issued or sold as of such particular time to employees, officers or directors of the Company pursuant to any long-term incentive plan duly adopted by the Board of Directors of the Company but excluding any reserve of shares of Common Stock or Common Stock Equivalents held by the Company for future issuances pursuant to or in connection with any such long term incentive plan.

(h)“MGA Agreements” means collectively, (i) the Managing General Agency Agreement, dated as of February 1, 2021, by and between Homesite Insurance Company and Bowhead Specialty Underwriters, Inc. (the “Agent”), as amended from time to time; (ii) the Amended and Restated Managing General Agency Agreement, dated April 1, 2022, by and between Homesite Insurance Company of Florida and the Agent, as amended from time to time; (iii) the Managing General Agency Agreement, dated February 1, 2021, by and between Midvale Indemnity Company and the Agent, as amended from time to time; and (iv) the Managing General Agency Agreement to be entered into in the second calendar quarter of 2024 by and between American Family Connect Reinsurance Company and the Agent, as amended from time to time.

(i)“OTC” means the Financial Industry Regulatory Authority OTC Bulletin Board electronic interdealer quotation system, the OTC Markets Group Inc. electronic interdealer quotation system, including OTCQX, OTCQB and OTC Pink, or any similar quotation system or association.

(j)“Principal Market” means the primary national securities exchange on which the Common Stock is then traded.

(k)“Reinsurance Agreement” means the 100% Quota Share Reinsurance Agreement, dated as of January 1, 2021, by and between the Holder and Bowhead Insurance Company Inc., as amended from time to time.

(l)“Reorganization Transaction” means the termination, liquidation and dissolution of Bowhead Insurance Holdings LP (“BIHL”), pursuant to which each of the holders of the Class A Interests and Class P Interests of BIHL (each as defined in the Amended and Restated Limited Partnership Agreement of BIHL, dated as of October 14, 2020, by and among the partners thereto, as amended from time to time (the “BIHL LPA”)) will receive a number of shares of Common Stock in accordance with the distribution provisions of the BIHL LPA.

(m)“Trading Day” means (i) any day on which the Common Stock is listed or quoted and traded on its Principal Market, (ii) if the Common Stock is not then listed or quoted and traded on any national securities exchange, then a day on which trading occurs on the OTC, or (iii) if trading does not occur on the OTC, any Business Day.

(n)“Transfer” means to, directly or indirectly, sell, hypothecate, pledge, offer to sell, contract to sell, sell or grant any option, right or warrant to purchase, purchase or acquire any option to sell, or otherwise dispose or transfer any security.

2.EXERCISE OF WARRANT.

(a)Number of Warrant Shares. On the date of any closing of the Over-allotment Option, the number of Warrant Shares available hereunder shall automatically be increased by a number of shares of Common Stock equal to five percent (5%) of the number of shares of Common Stock issued pursuant to the Over-allotment Option. The Company shall, at the request of a Holder and upon surrender of this Warrant at any time prior to the expiration of this Warrant, deliver to the Holder a new Warrant evidencing the rights of the Holder to purchase the increased number of Warrant Shares called for by this Section 2(a), which new Warrant shall in all other respects be identical with this Warrant, including with respect to the Issuance Date. For the avoidance of doubt, any increase in Warrant Shares available hereunder pursuant to this Section 2(a) shall have no effect on the vesting schedule of this Warrant.

(b)Exercise Price.    The exercise price per share of Common Stock under this Warrant shall be $17.00 per share, subject to adjustment pursuant to Section 3 hereof (the “Exercise Price”). Upon exercise, an amount equal to the Exercise Price multiplied by the number of Warrant Shares as to which all or a portion of this Warrant is being exercised (the “Aggregate Exercise Price”) shall be payable to the Company by wire transfer of immediately available funds to an account designated in writing by the Company; provided, however, that the Holder may elect to receive, upon such exercise the “net number” of shares of Common Stock, whereby the Company will withhold a number of Warrant Shares (subject to Section 2(d)(v) hereof) then issuable upon exercise of this warrant with an aggregate Fair Market Value as of the date of the Exercise Notice (as defined in Section 2(b) hereof) equal to such Aggregate Exercise Price (a “Cashless Exercise”).

(c)Exercise of Warrant.    Subject to the terms and conditions hereof, including the vesting requirements, the purchase rights represented by this Warrant may be exercised in whole or in part at any time or times during the Exercise Period by delivery of a written notice, in the form attached hereto as Exhibit A (the “Exercise Notice”), of the Holder’s election to exercise this Warrant. The Holder shall not be required to deliver the original Warrant in order to effect an exercise hereunder until the Holder has purchased all of the Warrant Shares available hereunder and this Warrant has been exercised in full, in which case, the Holder shall surrender this Warrant to the company for cancellation within three (3) Trading Days of the date on which the final

Exercise Notice is delivered to the Company; provided, however, that the Holder may surrender this Warrant and receive a new Warrant pursuant to Section 2(d)(ii) hereof. Partial exercises of this Warrant resulting in purchases of a portion of the total number of Warrant Shares available hereunder shall have the effect of lowering the outstanding number of Warrant Shares purchasable hereunder in an amount equal to the applicable number of Warrant Shares purchased. On or before the date that is the earlier of (i) two (2) Trading Days after the delivery to the Company of the Exercise Notice, and (ii) the number of trading days comprising the Standard Settlement Period after delivery to the Company of the Exercise Notice (such date, the “Warrant Share Delivery Date”), the Holder shall deliver to the Company the Aggregate Exercise Price in the form determined by the Company pursuant to Section 2(a) unless the purchase shall be consummated pursuant to a Cashless Exercise. As used herein, “Standard Settlement Period” means the standard settlement period, expressed in a number of Trading Days, on the Company’s Principal Market with respect to the Common Stock as in effect on the date of delivery of the Exercise Notice.

(d)Mechanics of Exercise.

(i)Delivery of Warrant Shares Upon Exercise.    Subject to the Company’s timely receipt of the Aggregate Exercise Price (as applicable), the Company shall cause the Warrant Shares purchased hereunder to be transmitted by the transfer agent to the Holder by book entry position, registered in the Company’s share register in the name of the Holder or its designee, for the number of Warrant Shares to which the Holder is entitled pursuant to such Exercise Notice by the Warrant Share Delivery Date. Upon delivery of the Exercise Notice and the Aggregate Purchase Price (as applicable), the Holder shall be deemed for all corporate purposes to have become the holder of record of the Warrant Shares with respect to which this Warrant has been exercised, irrespective of the date of delivery of the Warrant Shares; provided, that payment is received no later than the Warrant Share Delivery Date. In no event shall the Company be required to deliver any Warrant Shares prior to receipt of the Aggregate Exercise Price in respect of such Warrant Shares unless the purchase shall be consummated pursuant to a Cashless Exercise. The Holder and the Company shall maintain records showing the number of Warrant Shares purchased and the date of such purchases.

(ii)Delivery of New Warrant Upon Exercise.    If this Warrant shall have been exercised in part, the Company shall, at the request of a Holder and upon surrender of this Warrant at any time prior to the expiration of this Warrant, deliver to the Holder a new Warrant evidencing the rights of the Holder to purchase the unpurchased Warrant Shares called for by this Warrant, which new Warrant shall in all other respects be identical with this Warrant.

(iii)Rescission Rights.    If the Company fails to cause its transfer agent to transmit to the Holder the respective shares of Common Stock by the respective Warrant Share Delivery Date, then the Holder will have the right to rescind such exercise in Holder’s sole discretion.

(iv)Conditional Exercise.    Notwithstanding the foregoing, if an exercise of all or any portion of this Warrant is to be made in connection with a Fundamental Transaction, such exercise may, at the election of the Holder, be conditioned upon the consummation of such Fundamental Transaction. If the exercise of this Warrant is conditioned upon the consummation of a Fundamental Transaction, the Warrant Share Delivery Date shall be the date of such consummation and such exercise shall be deemed to be effective immediately prior to such consummation.

(v)No Fractional Shares.    No fractional shares shall be issued upon the exercise of this Warrant as a consequence of any adjustment pursuant hereto. All Warrant Shares (including fractions) issuable upon exercise of this Warrant may be aggregated for purposes of determining whether the exercise would result in the issuance of any fractional share. If, after aggregation, the exercise would result in the issuance of a fractional share, the Company shall, at its election, either pay a cash adjustment in respect of such final fraction in an amount equal to such fraction multiplied by the Exercise Price or round the number of shares issuable to the nearest whole share.

3.ADJUSTMENTS.    The Exercise Price and the number of Warrant Shares shall be adjusted from time to time as follows:

(a)Subdivision or Combination of Common Stock.    If the Company at any time on or after the Issuance Date subdivides (by any stock split, stock dividend, recapitalization or otherwise) one or more classes of its outstanding shares of Common Stock into a greater number of shares, the Exercise Price in effect immediately prior to such subdivision will be proportionately reduced and the number of Warrant Shares will be proportionately increased. If the Company at any time on or after the Issuance Date combines (by combination, reverse stock split or otherwise) one or more classes of its outstanding shares of Common Stock into a smaller number of shares, the Exercise Price in effect immediately prior to such combination will be proportionately increased and the number of Warrant Shares will be proportionately decreased. Any adjustment under this Section 3(a) shall become effective at the close of business on the date the subdivision or combination becomes effective. Each such adjustment of the Exercise Price shall be calculated to the nearest one-hundredth of a cent. Such adjustment shall be made successively whenever any event covered by this Section 3(a) shall occur.

(b)Fundamental Transactions.    If, at any time while this Warrant is outstanding, (i) the Company effects any merger of the Company with or into another entity and the Company is not the surviving entity (such surviving entity, the “Successor Entity”), (ii) the Company effects any sale of all or substantially all of its assets in one or a series of related transactions, (iii) any tender offer or exchange offer (whether by the Company or by another individual or entity, and approved by the Company) is completed pursuant to which holders of Common Stock are permitted to tender or exchange their shares of Common Stock for other securities, cash or property and the holders of at least 50% of the Common Stock accept such offer, or (iv) the Company effects any reclassification of the Common Stock or any compulsory share exchange pursuant to which the Common Stock is effectively converted into or exchanged for other securities, cash or property (other than as a result of a subdivision or combination of shares of Common Stock) (in any such case, a “Fundamental Transaction”), then, upon any subsequent exercise of this Warrant, the Holder shall have the right to receive per Warrant Share exercised the number of shares of Common Stock of the Successor Entity or of the Company and any other consideration, as applicable, received by a holder of a share of Common Stock in such Fundamental Transaction (the “Alternate Consideration”) receivable upon or as a result of such reorganization, reclassification, merger, consolidation, tender offer or disposition of assets by a holder of the number of shares of Common Stock for which this Warrant is exercisable immediately prior to such event. For purposes of any such exercise, the determination of the Exercise Price shall be appropriately adjusted to apply to such Alternate Consideration based on the amount of Alternate Consideration issuable in respect of one share of Common Stock in such Fundamental Transaction, and the Company shall apportion the Exercise Price among the Alternate Consideration in a reasonable manner reflecting the relative value of any different components of the Alternate Consideration. If holders of Common Stock are given any choice as to the securities, cash or property to be received in a Fundamental Transaction, then the Holder shall be given the same choice as to the Alternate Consideration it receives upon any exercise of this Warrant following such Fundamental Transaction. As a condition to any such Fundamental Transaction, any Successor Entity in such Fundamental Transaction shall issue to the Holder a new warrant consistent with the foregoing provisions and evidencing the Holder’s right to exercise such warrant into Alternate Consideration.

(c)Calculations.    All calculations under this Section 3 shall be made to the nearest cent or the nearest 1/100th of a share, as the case may be. For purposes of this Section 3, the number of shares of Common Stock deemed to be issued and outstanding as of a given date shall be the sum of the number of shares of Common Stock (excluding treasury shares, if any) issued and outstanding.

4.TRANSFERABILITY.    This Warrant may not be Transferred or assigned (whether by operation of law or otherwise) except to a person (including any successor of the Holder) who is controlled and majority owned by American Family Insurance Mutual Holding Company, a Wisconsin mutual insurance holding company and the ultimate controlling entity of the Holder.

Company will give the Holder not less than twenty (20) days’ advance written notice of a transaction in the event of a Change of Control.

6.MISCELLANEOUS.

(a)Non-Circumvention.    The Company covenants and agrees that it will not, by amendment of its certificate of incorporation, bylaws or through any reorganization, transfer of assets, consolidation, merger, scheme of arrangement, dissolution, issue or sale of securities, or any other voluntary action, avoid or seek to avoid the observance or performance of any of the terms of this Warrant, and will at all times in good faith carry out all the provisions of this Warrant and take all action as may be required to protect the rights of the Holder. Without limiting the generality of the foregoing, the Company (i) shall not increase the par value of any shares of Common Stock receivable upon the exercise of this Warrant above the Exercise Price then in effect, (ii) shall take all such actions as may be necessary or appropriate in order that the Company may validly and legally issue fully paid and non-assessable shares of Common Stock upon the exercise of this Warrant, and (iii) shall, for so long as this Warrant is outstanding, have authorized and reserved, free from preemptive rights, a sufficient number of shares of Common Stock to provide for the issuance of the Warrant Shares upon full exercise of this Warrant (based on the Exercise Price in effect from time to time, and without regard to any limitations on exercise).

(b)Reissuance.

(i)Lost, Stolen or Mutilated Warrant.    If this Warrant is lost, stolen, mutilated or destroyed, the Company will, on such terms as to indemnity or otherwise as it may reasonably impose (which shall, in the case of a mutilated Warrant, include the surrender thereof), issue a new Warrant of like denomination and tenor as this Warrant so lost, stolen, mutilated or destroyed.

(ii)Issuance of New Warrants.    Whenever the Company is required to issue a new Warrant pursuant to the terms of this Warrant, including in connection with Sections 2(a) and 2(d)(ii) hereof, such new Warrant shall be of like tenor with this Warrant, and shall have an issuance date, as indicated on the face of such new Warrant which is the same as the Issuance Date.

(c)Warrant Holder Not Deemed Stockholder.    Except as otherwise specifically provided herein, this Warrant, in and of itself, shall not entitle the Holder to any voting rights or other rights as a stockholder of the Company. In addition, nothing contained in this Warrant shall be construed as imposing any liabilities on the Holder to purchase any securities (upon exercise of this Warrant or otherwise) or as a stockholder of the Company, whether such liabilities are asserted by the Company or by creditors of the Company.

(d)Accredited Investor.    The Holder represents and warrants that (i) it is an “accredited investor” as defined in Rule 501 of Regulation D promulgated under the Securities Act and was not organized for the purposes of acquiring this Warrant or the Warrant Shares or (ii) it is not a US Person as defined in Regulation S under the Securities Act and it will not exercise this Warrant on behalf of a US Person. The Holder’s financial condition is such that it is able to bear the risk of holding this Warrant or the Warrant Shares (as applicable) for an indefinite period of time and the risk of loss of its entire investment. The Holder has sufficient knowledge and experience in investing in companies similar to the Company so as to be able to evaluate the risks and merits of investment in the Company.

(e)Rule 144.    The Holder acknowledges that this Warrant and the Warrant Shares must be held indefinitely unless subsequently registered under the Securities Act or an exemption from such registration is available. The Holder is aware of the provisions of Rule 144 promulgated under the Securities Act which permit limited resale of shares purchased in a private placement subject to the satisfaction of certain conditions. The Holder acknowledges that, in the event all of the requirements of Rule 144 are not met, registration under the Securities Act or an exemption from registration will be required for any disposition of this Warrant or the Warrant Shares. This Warrant or such Warrant Shares may be offered, sold or otherwise disposed of in accordance with Rule 144 or 144A under the Act, provided that the Company shall have been furnished with such information as the Company may reasonably request to provide a reasonable assurance that the provisions of Rule 144 or 144A have been satisfied.

(f)Notices.

(i)Any and all notices or other communications or deliveries to be provided by the Holder hereunder including, without limitation, any Exercise Notice, shall be in writing and delivered personally or by email, or sent by a nationally recognized overnight courier service, addressed to the Company, at Bowhead Specialty Holdings Inc., 1411 Broadway, Suite 3800, New York, NY 10018, Attention: H. Matthew Crusey, General Counsel, e-mail address: mcrusey@bowheadspecialty.com, or such other email address or address as the company may specify for such purposes by notice to the Holder. Any and all notices or other communications or deliveries to be provided by the Company shall be in writing and delivered personally, by e-mail, or sent by a nationally recognized overnight courier service addressed to the Holder at the e-mail address or address of the Holder appearing on the books of the Company. Any notice or other communication or deliveries hereunder shall be deemed given and effective on the earlier of (A) the date of transmission, if such notice or communication is delivered via e-mail at the e-mail address set forth in this Section 6(f) prior to 5:30 p.m. eastern time on any date, (B) the next Trading Day after the date of transmission, if such notice or communication is delivered via e-mail at the e-mail address set forth in this Section 6(f) on a day that is not a Trading Day or later than 5:30 p.m. eastern time on any Trading Day, (C) the second Trading Day following the date of mailing, if sent by U.S. nationally recognized overnight courier service, or (D) upon actual receipt by the party to whom such notice is required to be given.

(ii)The Company shall provide the Holder with prompt written notice (i) immediately upon any adjustment of the Exercise Price, setting forth in reasonable detail, the calculation of such adjustment and (ii) at least twenty days prior to the date on which the Company closes its books or takes a record (A) with respect to any dividend or distribution upon the shares of Common Stock or (B) for determining rights to vote with respect to any Fundamental Transaction, dissolution or liquidation, provided in each case that such information shall be made known to the public prior to or in conjunction with such notice being provided to the Holder.

(g)Governing Law and Venue.    This Warrant shall be governed by and construed in accordance with the laws of the State of Delaware without regard to principles of conflicts of laws. Each of the Parties hereby irrevocably and unconditionally (a) submits, for itself and its property, to the exclusive jurisdiction and venue of the Delaware Court of Chancery (or, only if the Delaware Court of Chancery does not have jurisdiction over a particular matter, the Superior Court of the State of Delaware (and the Complex Commercial Litigation Division thereof if such division has jurisdiction over the particular matter), or if the Superior Court of the State of Delaware does not have jurisdiction, any federal court of the United States of America sitting in the State of Delaware) (“Delaware Courts”), and any appellate court from any decision thereof, in any Action arising out of or relating to this Warrant, including the negotiation, interpretation, execution or performance of this Warrant and agrees that all claims in respect of any such Action shall be heard and determined in the Delaware Courts, (b) waives, to the fullest extent it may legally and effectively do so, any objection which it may now or hereafter have to the laying of venue of any Action arising out of or relating to this Warrant or the negotiation, interpretation, execution or performance of this Warrant in the Delaware Courts, including any objection based on its place of incorporation or domicile, (c) waives, to the fullest extent permitted by Law, the defense of an inconvenient forum to the maintenance of such Action in any such court and (d) agrees that a final judgment in any such Action shall be conclusive and may be enforced in other jurisdictions by suit on the judgment or in any other manner provided by

law. Each of the parties consents and agrees that service of process, summons, notice or document for any action permitted hereunder may be delivered by registered mail addressed to it at the applicable address set forth in Section 6(f) or in any other manner permitted by applicable law.

(h)Waiver of Jury Trial. EACH OF THE PARTIES ACKNOWLEDGES AND AGREES THAT ANY CONTROVERSY THAT MAY BE BASED UPON, ARISING OUT OF OR RELATED TO THIS AGREEMENT IS LIKELY TO INVOLVE COMPLICATED AND DIFFICULT ISSUES AND, THEREFORE, EACH SUCH PARTY HEREBY IRREVOCABLY AND UNCONDITIONALLY WAIVES ANY RIGHT SUCH PARTY MAY HAVE TO A TRIAL BY JURY FOR ANY DISPUTE BASED UPON, ARISING OUT OF OR RELATING TO THIS AGREEMENT OR THE BREACH, TERMINATION OR VALIDITY HEREOF OR ANY TRANSACTIONS CONTEMPLATED BY THIS AGREEMENT. EACH OF THE PARTIES CERTIFIES AND ACKNOWLEDGES THAT (A) NEITHER THE OTHER PARTIES NOR THEIR RESPECTIVE REPRESENTATIVES, AGENTS OR ATTORNEYS HAVE REPRESENTED, EXPRESSLY OR OTHERWISE, THAT SUCH OTHER PARTY WOULD NOT, IN THE EVENT OF LITIGATION, SEEK TO ENFORCE THE FOREGOING WAIVER, (B) EACH OF THE PARTIES UNDERSTANDS AND HAS CONSIDERED THE IMPLICATIONS OF THIS WAIVER, (C) EACH OF THE PARTIES MAKES THIS WAIVER VOLUNTARILY AND (D) EACH OF THE PARTIES HAS BEEN INDUCED TO ENTER INTO THIS AGREEMENT BY, AMONG OTHER THINGS, THE MUTUAL WAIVERS AND CERTIFICATIONS OF THIS SECTION 6(H). ANY PARTY MAY FILE AN ORIGINAL COUNTERPART OR A COPY OF THIS AGREEMENT WITH ANY COURT AS WRITTEN EVIDENCE OF THE CONSENT OF THE PARTIES TO THE WAIVER OF THEIR RIGHT TO TRIAL BY JURY.

(i)Specific Performance. Each party hereto acknowledges and agrees that any breach of this Warrant would result in substantial harm to the other party hereto for which monetary damages alone could not adequately compensate. Therefore, the parties hereto unconditionally and irrevocably agree that any non-breaching party hereto shall be entitled to seek protective orders, injunctive relief and other remedies available at law or in equity (including, without limitation, seeking specific performance).

(j)No Third Party Beneficiaries.    This Warrant and the rights and obligations evidenced hereby shall inure solely to the benefit of and be binding upon the Company and the Holder. No person or entity shall be deemed to possess any third-party beneficiary right pursuant to this Warrant.

(k)Amendment and Waiver.    The terms of this Warrant may be amended or waived (either generally or in a particular instance and either retroactively or prospectively) only with the written consent of the Company and the Holder.

(l)Severability.    Wherever possible, each provision of this Warrant shall be interpreted in such manner as to be effective and valid under applicable law, but if any provision of this Warrant shall be prohibited by or invalid under applicable law, such provision shall be ineffective to the extent of such prohibition or invalidity, without invalidating the remainder of such provisions or the remaining provisions of this Warrant.

(m)Headings.    The headings used in this Warrant are for the convenience of reference only and shall not, for any purpose, be deemed a part of this Warrant.

(n)Entire Agreement.    This Warrant constitutes the entire agreement between the parties with respect to the subject matter hereof and supersedes (A) all prior oral or written proposals or agreements, (B) all contemporaneous oral proposals or agreements, and (C) all previous negotiations and all other communications or understandings between the parties, in each case with respect to the subject matter hereof.

IN WITNESS WHEREOF, the Company has caused this Warrant to be duly executed as of the Issuance Date set forth above.

(To be executed by the registered holder to exercise this Common Stock Purchase Warrant)

THE UNDERSIGNED holder hereby exercises the right to purchase ____________ shares of Common Stock (“Warrant Shares”) of Bowhead Specialty Holdings Inc., a Delaware corporation (the “Company”), evidenced by the attached copy of the Common Stock Purchase Warrant to the extent evidenced in full (the “Warrant”) and tenders herewith payment of the exercise price in full, together with all applicable transfer taxes, if any. Capitalized terms used herein and not otherwise defined shall have the respective meanings set forth in the Warrant.

1.Payment of Exercise Price. Payment for the Warrant Shares shall be made in the form of (check applicable box):

☐ lawful money of the United States; or

☐ the cancellation of such number of Warrant Shares as is necessary, in accordance with the formula set forth in Section 2(b) of the Warrant for a Cashless Exercise.

2.Delivery of Warrant Shares. The Company shall deliver to the holder the aforementioned number of Warrant Shares in book-entry form in accordance with the terms of the Warrant.

3.Representations and Warranties. The undersigned hereby represents and warrants as follows: