Optimal Design of a Perpetual Equity-indexed Annuity

We find the participation rate, guaranteed death benefit, guaranteed surrender benefit, and initial and maintenance fees that most appeal to a buyer of a perpetual equity-indexed annuity (EIA) from the standpoint of maximizing the buyer’s expected discounted utility of wealth at death, also called bequest, while still allowing the issuer of the EIA to (at least) break even on the basis of the expected discounted value of the issuer’s payout. In calculating the buyer’s expected utility, we use the physical probability faced by the buyer. However, in calculating the expected value of the issuer’s payout, we use a type of risk-neutral probability by assuming that the issuer sells many independent policies. We demonstrate our method with an illustrative numerical example.