The insurance underwriter Hartford Life Inc. has long reigned as the largest provider of annuities sold by banks. But if Robert M. Devlin, chief executive officer of American General Financial Group, gets his way, bragging rights could soon shift to his Houston-based company.

"With our growth rate at banks, we do have a good shot of being No. 1,'' Mr. Devlin said in a recent interview. "Even if we don't do it this year, we are still going to bring in a lot of business.''

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