) -- A little bit of hope is all it takes to move

American International Group

(AIG) - Get Report

up these days.

Shares of the flailing insurer soared 21.5% to close at $48.52, after Bloomberg reported that the government may ease the terms of its bailout.

Rep. Edolphus Towns, Democrat chairman of the House Oversight and Government Reform Committee, has told the panel's staff to review a proposal put forward by former AIG Chief Executive Maurice "Hank" Greenberg to restructure the insurer's government rescue package, Bloomberg wrote.

The proposal would lower interest rates on government loads and give AIG more time to repay its $85 billion debt. It would also reduce the current 80% government stake in the company.

Separately, a report released today by the Government Accountability Office, which oversees Treasury's $700 billion Troubled Asset Relief Program, said the ultimate success of AIG's restructuring and repayment efforts remains uncertain.

But there are some bright words amid the report -- such as "signs of stabilizing" and "some progress" -- that investors appear to be trading on.

Shares of AIG are returning to levels of late August, when the company rallied on some summer speculation.

-- Reported by Jeanine Poggi in New York

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