Exhibit 10.1

AMENDMENT NO. 1

TO THE INVESTOR RIGHTS AGREEMENT

This AMENDMENT NO. 1 TO THE INVESTOR RIGHTS AGREEMENT, dated June 8, 2017 (this “ Amendment ”), is made by Arch Capital Group Ltd., an exempted company with limited liability registered under the laws of Bermuda (together with its successors and permitted assigns, the “ Company ”), American International Group, Inc., a Delaware corporation (the “ Parent ”), American Home Assurance Company, a New York corporation (“ AHAC ”), Lexington Insurance Company, a Delaware corporation (“ Lexington ”), and National Union Fire Insurance Company of Pittsburgh, Pa., a Pennsylvania corporation (“ NUFIC ”). Capitalized terms not defined herein shall have the meanings set forth in the Investor Rights Agreement, dated December 31, 2016 (the “ Agreement ”), by and between the Company and the Parent.

WHEREAS, pursuant to the Joinders to the Agreement, dated January 18, 2017, by AHAC, Lexington and NUFIC, the parties hereto are parties to the Agreement, pursuant to which the parties have agreed to certain terms and conditions concerning the Parent’s and other Investors’ relationships with and investments in the Company, including the 1,276,282 Company Series D Preferred Shares convertible into 12,762,820 Company Common Shares (such Company Series D Preferred Shares, together with such Company Common Shares issuable by way of conversion thereof, the “ Convertible Preferred Shares ”) acquired by the Parent on December 31, 2016 pursuant to the Stock Purchase Agreement; and

WHEREAS, the parties hereto desire to amend the Agreement in accordance with Section 4.6 thereof, as hereinafter provided.

NOW, THEREFORE, in consideration of the mutual covenants contained herein and other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto agree as follows:

1. Amendments to Agreement .

1.1.      Amendments to Section 2.1 .

(i)      Section 2.1 of the Agreement is hereby amended by amending and restating Subsection 2.1(a) in its entirety as follows:

(a)    Other than Permitted Transfers, neither the Parent nor any Investor shall Transfer any Convertible Preferred Shares until January 15, 2018 (such date, the “ Restricted Period Termination Date ”); provided that the Parent or any other Investor may Transfer any Convertible Preferred Shares, not counting Convertible Preferred Shares that are Transferred pursuant to a Permitted Transfer, up to an aggregate amount equal to 638,141 of the Original Convertible Preferred Shares during the First Restricted Period, and up to an additional 95,721 of the Original Convertible Preferred Shares during the First Restricted Period to the extent that the several underwriters exercise the option to purchase additional securities expected to be granted to the underwriters pursuant to a Purchase Agreement between the Company, the Parent, the Investors party thereto and the several underwriters party thereto providing for an offering and sale of Company Common Shares by the Parent and one or more other Investors.

(ii)      Section 2.1 of the Agreement is hereby amended by deleting the words “or the Twelve-Month Restricted Period” in Section 2.1(c).

1.2.      Amendments to Section 4.6 .

(i)     The definition of “Six-Month Restricted Date” is hereby amended and restated in its entirety as follows:

“ First Restricted Date ” means the date of Amendment No. 1 to this Agreement.

(ii)     The definition of “Six-Month Restricted Period” is hereby amended and restated in its entirety as follows:

“ First Restricted Period ” means the period from and including the First Restricted Date to and including the date prior to the Restricted Period Termination Date.

(iii)     The definitions of “Twelve-Month Restricted Date” and “Twelve-Month Restricted Period” and all references in the Agreement thereto are hereby deleted.

1.3.      Other Amendments .

(i)     The Agreement is hereby amended by replacing all occurrences of the term “Six-Month Restricted Date” with “First Restricted Date”.

(ii)     The Agreement is hereby amended by replacing all occurrences of the term “Six-Month Restricted Period” with “First Restricted Period”.

2.      Miscellaneous . Any reference in the Agreement to “this Agreement”, “hereunder”, “hereof”, “herein” or words of like import shall hereafter be deemed to refer to the Agreement as hereby amended. Except as expressly amended herein, the parties hereto hereby agree and acknowledge that all of the terms and provisions set forth in the Agreement remain in full force and effect in all respects. To the extent of any inconsistency between the provisions of this Amendment and the provisions of the Agreement, the terms of this Amendment shall govern. This Amendment shall be governed and construed in accordance with the Agreement.

3.      General Provisions . The provisions of Sections 4.2 ( Notices ), 4.4 ( No Partnership ), 4.5 ( Memorandum of Association ), 4.6 ( Amendments and Waivers ), 4.8 ( Assignment ), 4.9 ( Severability ), 4.11 ( Entire Agreement ), 4.12 ( Governing Law; Arbitration; Waiver of Jury Trial ), 4.14 ( Specific Performance ) and 4.15 ( No Third Party Beneficiaries ) of the Agreement shall apply to this Amendment mutatis mutandis .

4.      Counterparts . This Amendment may be signed in any number of counterparts (including by facsimile or PDF), each of which shall be an original, with the same effect as if the signatures thereto and hereto were upon the same instrument. This Amendment shall become effective when the parties hereto shall have received a counterpart hereof signed by each other party hereto.

Signature Page Follows

IN WITNESS WHEREOF, each of the parties hereto has caused this Amendment to be duly executed by its authorized representatives as of the day and year first above written.