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Optimal surrender strategies for equity-indexed annuity investors with partial information. (English) Zbl 1246.91121

Summary: In this paper we consider an equity-indexed annuity (EIA) investor who wants to determine when he should surrender the EIA in order to maximize his logarithmic utility of the wealth at surrender time. We model the dynamics of the index using a geometric Brownian motion with regime switching. To be more realistic, we consider a finite time horizon and assume that the Markov chain is unobservable. This leads to the optimal stopping problem with partial information. We give a representation of the value function and an integral equation satisfied by the boundary. In the Bayesian case which is a special case of our model, we obtain analytical results for the value function and the boundary.

MSC:

91G10 Portfolio theory
91B06 Decision theory
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References:

[1] Cheung, K.; Yang, H., Optimal stopping behavior of equity-linked investment products with regime switching, Insurance: Mathematics and Economics, 37, 599-614 (2005) · Zbl 1129.60065
[2] Décamps, J.-P.; Mariotti, T.; Villeneuve, S., Investment timing under incomplete information, Mathematics of Operations Research, 30, 2, 472-500 (2005) · Zbl 1082.91048
[3] Ekström, E.; Lu, B., Optimal selling of an asset under incomplete information, International Journal of Stochastic Analysis, 2011, 17 pp (2011), Article ID 543590 · Zbl 1230.91168
[4] Elliott, R. J., Stochastic Calculus and Applications (1982), Springer: Springer Berlin · Zbl 0503.60062
[5] Friedman, A., Stochastic Differential Equations and Applications I (1975), Academic Press: Academic Press New York
[6] Hardy, M., Investment Guarantees: The New Science of Modeling and Risk Management for Equity-Linked Insurance (2003), John Wiley: John Wiley New York
[7] Jacka, S., Optimal stopping and the American put, Mathematical Finance, 1, 2, 1-14 (1991) · Zbl 0900.90109
[8] Karatzas, I.; Shreve, S., Brownian Motion and Stochastic Calculus (1991), Springer-Verlag: Springer-Verlag New York · Zbl 0734.60060
[9] Karatzas, I.; Shreve, S., Methods of mathematical Finance (1998), Springer-Verlag: Springer-Verlag New York · Zbl 0941.91032
[10] Klein, M., Comment on investment timing under incomplete information, Mathematics of Operations Research, 34, 1, 249-254 (2009) · Zbl 1213.60083
[11] Lin, X.; Tan, K., Valuation of equity-indexed annuities under stochastic interest rates, North American Actuarial Journal, 7, 4, 72-91 (2003) · Zbl 1084.60530
[12] Lipster, R. S.; Shiryaev, A. N., Statistics of Random Processes I General Theory (2001), Springer-Verlag: Springer-Verlag New York
[13] Moore, K., Optimal surrender strategies for equity-indexed annuity investors, Insurance: Mathematics and Economics, 44, 1-18 (2009) · Zbl 1156.91379
[14] Moore, K.; Young, V., Pricing equity-indexed pure endowments via the principle of equivalent utility, Insurance: Mathematics and Economics, 33, 497-516 (2003) · Zbl 1103.91370
[15] Moore, K.; Young, V., Optimal design of a perpetual equity-indexed annuity, North American Actuarial Journal, 9, 1, 57-72 (2005) · Zbl 1085.60512
[16] Peskir, G., On the American option problem, Mathematical Finance, 15, 169-181 (2005) · Zbl 1109.91028
[17] Peskir, G.; Shiryaev, A., Optimal Stopping and Free-Boundary Problems (2006), Birkhäuser: Birkhäuser Basel · Zbl 1115.60001
[18] Rishel, R., Whether to sell or hold a stock, Communications in Information and Systems, 6, 193-202 (2001) · Zbl 1132.93351
[19] Tiong, S., Valuing equity-indexed annuities, North American Actuarial Journal, 4, 4, 149-163 (2000) · Zbl 1083.62545
[20] Yuen, F. L.; Yang, H., pricing asian options and equity-indexed annuities with regime switching by the trinomial tree method, North American Actuarial Journal, 14, 2, 256-277 (2010) · Zbl 1219.91145
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