It may have been written off as a hopeless case less than a year ago, but the stock of the American International Group shot up to $50 on Thursday, capping a fourfold gain in the last two months.

The recently selected chief of A.I.G., Robert Benmosche, said he would rely on the ousted chief, Maurice R. Greenberg, for advice.

Go to your Portfolio »

For all the optimism taking hold in the markets these days, it is hard to find a tangible explanation.

“Who would want to buy a stock that’s still 80 percent owned by the government?” wondered William T. Fitzpatrick, an equity analyst at Optique Capital. Shares ended the day at $47.84, a gain of 27 percent from the previous close of $37.69.

Yes,...