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Optimal Design of a Perpetual Equity-Indexed Annuity

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  • Kristen Moore
  • Virginia Young

Abstract

We find the participation rate, guaranteed death benefit, guaranteed surrender benefit, and initial and maintenance fees that most appeal to a buyer of a perpetual equity-indexed annuity (EIA) from the standpoint of maximizing the buyer’s expected discounted utility of wealth at death, also called bequest, while still allowing the issuer of the EIA to (at least) break even on the basis of the expected discounted value of the issuer’s payout. In calculating the buyer’s expected utility, we use the physical probability faced by the buyer. However, in calculating the expected value of the issuer’s payout, we use a type of risk-neutral probability by assuming that the issuer sells many independent policies. We demonstrate our method with an illustrative numerical example.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:uaajxx:v:9:y:2005:i:1:p:57-72
    DOI: 10.1080/10920277.2005.10596184
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    Cited by:

    1. Martin Eling & Michael Kochanski, 2013. "Research on lapse in life insurance: what has been done and what needs to be done?," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 14(4), pages 392-413, August.
    2. Hongzhong Zhang, 2018. "Stochastic Drawdowns," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 10078, August.
    3. Boyle, Phelim & Tian, Weidong, 2008. "The design of equity-indexed annuities," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 303-315, December.
    4. 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.
    5. 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.
    6. Moore, Kristen S., 2009. "Optimal surrender strategies for equity-indexed annuity investors," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 1-18, February.
    7. Zhang, Hongzhong & Leung, Tim & Hadjiliadis, Olympia, 2013. "Stochastic modeling and fair valuation of drawdown insurance," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 840-850.

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