Abstract

Equity-indexed annuity (EIA) products are becoming more and more popular since they were first introduced in 1995. The growing popularity stems from the fact that the EIAs allow investors to earn part or all the equity accumulated and enjoy a minimum guaranteed growth rate on the principal. An EIA investor may consider surrendering the contract before maturity and invest in the stock index in order to earn the full stock growth. He may also invest in a risk-free asset for protection from downside risk. We consider an EIA policyholder who seeks the optimal surrender strategy, and asset allocation strategy after surrender, in order to maximize his expected discounted utility at expiration of the contract that is either the maturity or his time of death, whichever comes first. We derive the Hamilton-Jacobi-Bellman equations, satisfied by the optimal value function, and derive the optimal strategies. We find that the optimal surrender strategies appear in the form of a continuation region or two surrender boundaries. That is, the investor stays in the contract when the contract value is within the region. We also study the impact of product features, market assumptions and individual behavior patterns on the surrender boundaries