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Optimal surrender strategies for equity-indexed annuity investors with partial information

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  • Wei, Jiaqin
  • Wang, Rongming
  • Yang, Hailiang

Abstract

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.

Suggested Citation

  • Wei, Jiaqin & Wang, Rongming & Yang, Hailiang, 2012. "Optimal surrender strategies for equity-indexed annuity investors with partial information," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1251-1258.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:7:p:1251-1258
    DOI: 10.1016/j.spl.2012.03.021
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    References listed on IDEAS

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    1. X. Sheldon Lin & Ken Seng Tan, 2003. "Valuation of Equity-Indexed Annuities Under Stochastic Interest Rates," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(4), pages 72-91.
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    5. Moore, Kristen S., 2009. "Optimal surrender strategies for equity-indexed annuity investors," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 1-18, February.
    6. Kristen Moore & Virginia Young, 2005. "Optimal Design of a Perpetual Equity-Indexed Annuity," North American Actuarial Journal, Taylor & Francis Journals, vol. 9(1), pages 57-72.
    7. Serena Tiong, 2000. "Valuing Equity-Indexed Annuities," North American Actuarial Journal, Taylor & Francis Journals, vol. 4(4), pages 149-163.
    8. Fei Yuen & Hailiang Yang, 2010. "Pricing Asian Options and Equity-Indexed Annuities with Regime Switching by the Trinomial Tree Method," North American Actuarial Journal, Taylor & Francis Journals, vol. 14(2), pages 256-272.
    9. Goran Peskir, 2005. "On The American Option Problem," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 169-181, January.
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    2. Xing, Jie & Ma, Jingtang & Yang, Wensheng, 2023. "Optimal entry decision of unemployment insurance under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 31-52.

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