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Analytic Solution for Return of Premium and Rollup Guaranteed Minimum Death Benefit Options Under Some Simple Mortality Laws

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  • Ulm, Eric R.

Abstract

Much attention has been focused recently on the issue of valuing guaranteed minimum death benefits embedded in annuity contracts. These benefits resemble a sequence of put options and their value should obey a differential equation similar to the Black-Scholes equation for simple put options. This paper derives a number of analytic solutions to this equation for a number of simple mortality laws.

Suggested Citation

  • Ulm, Eric R., 2008. "Analytic Solution for Return of Premium and Rollup Guaranteed Minimum Death Benefit Options Under Some Simple Mortality Laws," ASTIN Bulletin, Cambridge University Press, vol. 38(2), pages 543-563, November.
    • Handle: RePEc:cup:astinb:v:38:y:2008:i:02:p:543-563_01
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    Citations

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    Cited by:

    1. Anne MacKay & Maciej Augustyniak & Carole Bernard & Mary R. Hardy, 2017. "Risk Management of Policyholder Behavior in Equity-Linked Life Insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(2), pages 661-690, June.
    2. Feng, Runhuan & Huang, Huaxiong, 2016. "Statutory financial reporting for variable annuity guaranteed death benefits: Market practice, mathematical modeling and computation," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 54-64.
    3. Feng, Runhuan & Shimizu, Yasutaka, 2016. "Applications of central limit theorems for equity-linked insurance," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 138-148.
    4. Ulm, Eric R., 2014. "Analytic solution for ratchet guaranteed minimum death benefit options under a variety of mortality laws," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 14-23.
    5. Runhuan Feng & Xiaochen Jing & Jan Dhaene, 2015. "Comonotonic Approximations of Risk Measures for Variable Annuity Guaranteed Benefits with Dynamic Policyholder Behavior," Tinbergen Institute Discussion Papers 15-008/IV/DSF85, Tinbergen Institute.
    6. Ulm, Eric, 2020. "Analytic Valuation of GMDB Options with Utility Based Asset Allocation," Working Paper Series 21060, Victoria University of Wellington, School of Economics and Finance.
    7. Feng, Runhuan & Yi, Bingji, 2019. "Quantitative modeling of risk management strategies: Stochastic reserving and hedging of variable annuity guaranteed benefits," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 60-73.
    8. Liang, Xiaoqing & Tsai, Cary Chi-Liang & Lu, Yi, 2016. "Valuing guaranteed equity-linked contracts under piecewise constant forces of mortality," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 150-161.
    9. Gerber, Hans U. & Shiu, Elias S.W. & Yang, Hailiang, 2015. "Geometric stopping of a random walk and its applications to valuing equity-linked death benefits," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 313-325.
    10. Wenguang Yu & Yaodi Yong & Guofeng Guan & Yujuan Huang & Wen Su & Chaoran Cui, 2019. "Valuing Guaranteed Minimum Death Benefits by Cosine Series Expansion," Mathematics, MDPI, vol. 7(9), pages 1-15, September.
    11. Yaodi Yong & Hailiang Yang, 2021. "Valuation of Cliquet-Style Guarantees with Death Benefits in Jump Diffusion Models," Mathematics, MDPI, vol. 9(16), pages 1-21, August.
    12. Wang, Yayun & Zhang, Zhimin & Yu, Wenguang, 2021. "Pricing equity-linked death benefits by complex Fourier series expansion in a regime-switching jump diffusion model," Applied Mathematics and Computation, Elsevier, vol. 399(C).
    13. Gerber, Hans U. & Shiu, Elias S.W. & Yang, Hailiang, 2012. "Valuing equity-linked death benefits and other contingent options: A discounted density approach," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 73-92.

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