A legal battle over nearly $ 20 billion of American International Group stock escalated yesterday , as lawyers for Maurice R. Greenberg , the company 's former chief executive , argued in a lawsuit that the shares belonged to Starr International , which is headed by Mr. Greenberg , and not to A.I.G . The lawsuit asks the court to recognize Starr International , which has provided long-term compensation to A.I.G . executives , as an independent entity .