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**Optimal stopping behavior of equity-linked investment products with regime switching.**
*(English)*
Zbl 1129.60065

Summary: 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.

### MSC:

60J20 | Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) |

60J10 | Markov chains (discrete-time Markov processes on discrete state spaces) |

60G40 | Stopping times; optimal stopping problems; gambling theory |

91B28 | Finance etc. (MSC2000) |

### Keywords:

equity-linked products; Markov regime switching model; optimal surrender time; stochastic orders; utility function
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\textit{K. C. Cheung} and \textit{H. Yang}, Insur. Math. Econ. 37, No. 3, 599--614 (2005; Zbl 1129.60065)

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