Underwrite

To bind oneself to support a project, usually by investing money; to insure; to sign one's name to a document, thereby assuming an obligation.

v. 1) to agree to pay an obligation which may arise from an insurance policy. 2) to guarantee purchase of all shares of stock or bonds being issued by a corporation, including an agreement to purchase by the underwriter if the public does not buy all the shares or bonds. 3) to guarantee by investment in a business or project.