Exhibit 99.1 JOINT FILING AND SOLICITATION AGREEMENT WHEREAS, certain of the undersigned are stockholders, direct or beneficial, of DWS Global High Income Fund, Inc., a Maryland corporation (the “Fund”); WHEREAS, Western Investment LLC, a Delaware limited liability company, Western Investment Hedged Partners L.P., a Delaware limited partnership, Western Investment Total Return Partners L.P., a Delaware limited partnership, Arthur D. Lipson, Robert H. Daniels, Gregory R. Dube and Neil Chelo, wish to form a group for the purpose of seeking representation on the Board of Directors of the Fund at the 2010 annual meeting of stockholders of the Fund, or any other meeting of stockholders held in lieu thereof, and any adjournments, postponements, reschedulings or continuations thereof (the “Annual Meeting”) and for soliciting stockholder support for any proposal submitted by Western Investment LLC to the Fund and for the purpose of taking all other action necessary to achieve the foregoing. NOW, IT IS AGREED, this 20th day of May, 2010 by the parties hereto: 1.In accordance with Rule 13d-1(k)(1)(iii) under the Securities Exchange Act of 1934, as amended (the “Exchange Act”), each of the undersigned (collectively, the “Group”) agrees to the joint filing on behalf of each of them of statements on Schedule 13D, and any amendments thereto, with respect to the securities of the Fund.Each member of the Group shall be responsible for the accuracy and completeness of his/its own disclosure therein, and is not responsible for the accuracy and completeness of the information concerning the other members, unless such member knows or has reason to know that such information is inaccurate. 2.So long as this agreement is in effect, each of the undersigned shall provide written notice to Olshan Grundman Frome Rosenzweig & Wolosky LLP (“Olshan”) of (i) any of their purchases or sales of securities of the Fund; or (ii) any securities of the Fund over which they acquire or dispose of beneficial ownership.Notice shall be given no later than 24 hours after each such transaction. 3.Each of the undersigned agrees to form the Group for the purpose of soliciting proxies or written consents for the election of the persons nominated by Western Investment to the Board of Directors of the Fund and any proposals submitted by Western Investment LLC to stockholders for their approval at the Annual Meeting and for the purpose of taking all other actions incidental to the foregoing. 4.Western Investment LLC shall have the right to pre-approve all expenses incurred in connection with the Group’s activities and agree to pay directly all such pre-approved expenses. 5.Each of the undersigned agrees that any SEC filing, press release or stockholder communication proposed to be made or issued by the Group or any member of the Group in connection with the Group’s activities set forth in Section 3 shall be first approved by Western Investment LLC, or its representatives, which approval shall not be unreasonably withheld. 6.The relationship of the parties hereto shall be limited to carrying on the business of the Group in accordance with the terms of this Agreement.Such relationship shall be construed and deemed to be for the sole and limited purpose of carrying on such business as described herein.Nothing herein shall be construed to authorize any party to act as an agent for any other party, or to create a joint venture or partnership, or to constitute an indemnification.Nothing herein shall restrict any party’s right to purchase or sell securities of the Fund, as he/it deems appropriate, in his/its sole discretion, provided that all such sales are made in compliance with all applicable securities laws. 7.This Agreement may be executed in counterparts, each of which shall be deemed an original and all of which, taken together, shall constitute but one and the same instrument, which may be sufficiently evidenced by one counterpart. 8.In the event of any dispute arising out of the provisions of this Agreement or their investment in the Fund, the parties hereto consent and submit to the exclusive jurisdiction of the Federal and State Courts in the State of New York. 9.Any party hereto may terminate his/its obligations under this Agreement on 24 hours’ written notice to all other parties, with a copy by fax to Adam Finerman at Olshan, Fax No. 902-784-2733. 10.Each party acknowledges that Olshan shall act as counsel for both the Group and Western Investment LLC and its affiliates relating to their investment in the Fund. 11.Each of the undersigned parties hereby agrees that this Agreement shall be filed as an exhibit to a Schedule 13D pursuant to Rule 13d-1(k)(1)(iii) under the Exchange Act. IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be executed as of the day and year first above written. WESTERN INVESTMENT LLC By: /s/ Arthur D. Lipson Name: Arthur D. Lipson Title: Managing Member WESTERN INVESTMENT HEDGED PARTNERS L.P. By: Western Investment LLC General Partner By: /s/ Arthur D. Lipson Name: Arthur D. Lipson Title: Managing Member WESTERN INVESTMENT TOTAL RETURN PARTNERS L.P. By: Western Investment LLC General Partner By: /s/ Arthur D. Lipson Name: Arthur D. Lipson Title: Managing Member /s/ Arthur D. Lipson ARTHUR D. LIPSON Individually and as Attorney-In-Fact for Robert H. Daniels, Gregory R. Dube and Neil Chelo

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