When Kevin Crowe looked at the demographics of people who buy fixed annuities and those who buy long-term-care policies, he noticed they were nearly identical.

“The average buyer is in their fifties, is middle or upper-middle class, and is obviously interested in both products,” said Mr. Crowe, chairman and chief executive officer of Essex Corp., a third-party marketer in New York. “I wondered: Why can’t we combine the two? So that’s what we did.”

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