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Abstract
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Sales of equity-indexed annuities (EIAs) increased dramatically to $6.4 billion in 2001 since their introduction in 1995. Under these contracts, the investor makes an initial deposit (or several deposits). During the deferral period, the interest accrual on the fund is linked to the performance of a stock or index. Generally, the investor earns reduced growth on the index in exchange for downside protection in the form of a minimum guarantee. In periods of high returns, an optimistic EIA owner might consider surrendering the EIA, perhaps paying a surrender charge, and investing the proceeds directly in a risk-free asset and the index to earn the full (versus reduced) index growth. We propose a variational inequality that governs the surrender strategy for an investor who wishes to maximize her expected utility of bequest. Under our assumptions on mortality and utility, we are able to solve the variational inequality analytically and recover the free boundary. Armed with an understanding of optimal policyholder behavior, we examine the contract features that are attractive to consumers and profitable for insurers. This paper is joint work with Virginia Young. |
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