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Optimal surrender strategies for equity-indexed annuity investors

  • Moore, Kristen S.
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    An equity-indexed annuity (EIA) is a hybrid between a variable and a fixed annuity that allows the investor to participate in the stock market, and earn at least a minimum interest rate. The investor sacrifices some of the upside potential for the downside protection of the minimum guarantee. Because EIAs allow investors to participate in equity growth without the downside risk, their popularity has grown rapidly. An optimistic EIA owner might consider surrendering an EIA contract, paying a surrender charge, and investing the proceeds directly in the index to earn the full (versus reduced) index growth, while using a risk-free account for downside protection. Because of the popularity of these products, it is important for individuals and insurers to understand the optimal policyholder behavior. We consider an EIA investor who seeks the surrender strategy and post-surrender asset allocation strategy that maximizes the expected discounted utility of bequest. We formulate a variational inequality and a Hamilton-Jacobi-Bellman equation that govern the optimal surrender strategy and post-surrender asset allocation strategy, respectively. We examine the optimal strategies and how they are affected by the product features, model parameters, and mortality assumptions. We observe that in many cases, the "no-surrender" region is an interval (wl,wu); i.e., that there are two free boundaries. In these cases, the investor surrenders the EIA contract if the fund value becomes too high or too low. In other cases, there is only one free boundary; the lower (or upper) surrender threshold vanishes. In these cases, the investor holds the EIA, regardless of how low (or high) the fund value goes. For a special case, we prove a succinct and intuitive condition on the model parameters that dictates whether one or two free boundaries exist.

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    File URL: http://www.sciencedirect.com/science/article/B6V8N-4T9CCP9-1/2/0f717c888504e18f40d8b02a2c13dd2b
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    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 44 (2009)
    Issue (Month): 1 (February)
    Pages: 1-18

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    Handle: RePEc:eee:insuma:v:44:y:2009:i:1:p:1-18
    Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505554

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    1. Huang, H. & Milevsky, M. A. & Wang, J., 2004. "Ruined moments in your life: how good are the approximations?," Insurance: Mathematics and Economics, Elsevier, vol. 34(3), pages 421-447, June.
    2. Olivia S. Mitchell & James M. Poterba & Mark J. Warshawsky, 1997. "New Evidence on the Money's Worth of Individual Annuities," NBER Working Papers 6002, National Bureau of Economic Research, Inc.
    3. Cheung, Ka Chun & Yang, Hailiang, 2005. "Optimal stopping behavior of equity-linked investment products with regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 599-614, December.
    4. Avner Friedman & Weixi Shen, 2002. "A variational inequality approach to financial valuation of retirement benefits based on salary," Finance and Stochastics, Springer, vol. 6(3), pages 273-302.
    5. Moshe A. Milevsky & Kristen S. Moore & Virginia R. Young, 2006. "Asset Allocation And Annuity-Purchase Strategies To Minimize The Probability Of Financial Ruin," Mathematical Finance, Wiley Blackwell, vol. 16(4), pages 647-671.
    6. Ranguelova, Elena & Feldstein, Martin, 2001. "Individual Risk in an Investment-Based Social Security System," Scholarly Articles 2797440, Harvard University Department of Economics.
    7. Friend, Irwin & Blume, Marshall E, 1975. "The Demand for Risky Assets," American Economic Review, American Economic Association, vol. 65(5), pages 900-922, December.
    8. Martin Feldstein & Elena Ranguelova, 2001. "Individual Risk in an Investment-Based Social Security System," American Economic Review, American Economic Association, vol. 91(4), pages 1116-1125, September.
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