Last summer, as financial markets swooned following an unprecedented downgrade of U.S. debt, Ajit Jain got a chance to walk in Warren Buffett's shoes.

Mr. Jain, who runs Berkshire Hathaway Inc.'s giant reinsurance division, made an unsolicited bid for Transatlantic Holdings Inc. The insurer had already agreed to a merger and was being circled by other potential suitors. But a drop in the value of those cash-and-stock proposals amid the U.S. debt crisis seemingly opened the door for an all-cash offer from Berkshire's Mr. Jain....