Optimal stopping behavior of equity-indexed annuity with regime switching

In recent years, there is a growing interest in equity-linked investment products. The return credited to such product depends on the return of some underlying reference index. A prominent example is the equity-indexed annuities (EIAs). A special feature of many of the equity-linked products is that the holders are entitled the right to surrender the product prior to maturity. In this paper, we will study the optimal surrender time for a equity-linked product in a discrete-time setting.We assume that the market environment will switch among different regimes in a Markovian way, and the return of the reference index will have different distributions in different regimes. Assuming a CRRA preference, we have obtained the optimal surrender policy. Properties of the optimal surrender behavior, in particular the effect of regime switching, are examined.