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Pricing Guaranteed Life Insurance Participating Policies with Annual Premiums and Surrender Option

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  • Anna Rita Bacinello

Abstract

This paper analyzes a life insurance endowment policy, paid by annual premiums, in which the benefit is annually adjusted according to the performance of a special investment portfolio and a minimum return is guaranteed to the policyholder. In particular, the author considers both the case in which the annual premium is constant and the case in which the premium also is adjusted according to the performance of the reference portfolio. Moreover, the policy under scrutiny is characterized by the presence of a surrender option, that is, of an American-style put option that enables the policyholder to give up the contract and receive the surrender value. The aim of the paper is to give sufficient conditions under which there exists a (unique) fair premium. This premium is implicitly defined by an equation (or, alternatively, can be viewed as a fixed point of a suitable function) based on a recursive binomial tree àla Cox, Ross, and Rubinstein (1979). An iterative algorithm is then implemented in order to compute it.

Suggested Citation

  • Anna Rita Bacinello, 2003. "Pricing Guaranteed Life Insurance Participating Policies with Annual Premiums and Surrender Option," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(3), pages 1-17.
    • Handle: RePEc:taf:uaajxx:v:7:y:2003:i:3:p:1-17
    DOI: 10.1080/10920277.2003.10596097
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    Citations

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    Cited by:

    1. Bernard, Carole & Boyle, Phelim P., 2011. "A Natural Hedge for Equity Indexed Annuities," Annals of Actuarial Science, Cambridge University Press, vol. 5(2), pages 211-230, September.
    2. Bernard Carole & Le Courtois Olivier, 2012. "Asset Risk Management of Participating Contracts," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 6(2), pages 1-23, June.
    3. Christian Hilpert & Jing Li & Alexander Szimayer, 2014. "The Effect of Secondary Markets on Equity-Linked Life Insurance With Surrender Guarantees," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 81(4), pages 943-968, December.
    4. Cheng, Chunli & Hilpert, Christian & Miri Lavasani, Aidin & Schaefer, Mick, 2023. "Surrender contagion in life insurance," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1465-1479.
    5. Siti Nurasyikin Shamsuddin & Noriszura Ismail & Nur Firyal Roslan, 2022. "What We Know about Research on Life Insurance Lapse: A Bibliometric Analysis," Risks, MDPI, vol. 10(5), pages 1-19, May.
    6. Schmeiser, H. & Wagner, J., 2011. "A joint valuation of premium payment and surrender options in participating life insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 580-596.
    7. Cheng, Chunli & Li, Jing, 2018. "Early default risk and surrender risk: Impacts on participating life insurance policies," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 30-43.
    8. Bernard, Carole & MacKay, Anne & Muehlbeyer, Max, 2014. "Optimal surrender policy for variable annuity guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 116-128.
    9. Ballotta, Laura, 2005. "A Lévy process-based framework for the fair valuation of participating life insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 173-196, October.
    10. Bernard, Carole & Kwak, Minsuk, 2016. "Semi-static hedging of variable annuities," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 173-186.
    11. Nadine Gatzert & Hato Schmeiser, 2008. "Assessing the Risk Potential of Premium Payment Options in Participating Life Insurance Contracts," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(3), pages 691-712, September.
    12. Gatzert, Nadine, 2008. "Asset management and surplus distribution strategies in life insurance: An examination with respect to risk pricing and risk measurement," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 839-849, April.
    13. Kleinow, Torsten & Willder, Mark, 2007. "The effect of management discretion on hedging and fair valuation of participating policies with maturity guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 445-458, May.
    14. Bacinello, Anna Rita, 2005. "Endogenous model of surrender conditions in equity-linked life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 270-296, October.
    15. Fard, Farzad Alavi & Siu, Tak Kuen, 2013. "Pricing participating products with Markov-modulated jump–diffusion process: An efficient numerical PIDE approach," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 712-721.
    16. Piotr Komański & Oskar Sokoliński, 2015. "Least-Squares Monte Carlo Simulation for Time Value of Options and Guarantees Calculation," Ekonomia journal, Faculty of Economic Sciences, University of Warsaw, vol. 41.
    17. Gerstner, Thomas & Griebel, Michael & Holtz, Markus & Goschnick, Ralf & Haep, Marcus, 2008. "A general asset-liability management model for the efficient simulation of portfolios of life insurance policies," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 704-716, April.
    18. Gerstner, Thomas & Griebel, Michael & Holtz, Markus, 2009. "Efficient deterministic numerical simulation of stochastic asset-liability management models in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 434-446, June.
    19. Gan, Guojun, 2013. "Application of data clustering and machine learning in variable annuity valuation," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 795-801.
    20. Barbarin, Jerome & Devolder, Pierre, 2005. "Risk measure and fair valuation of an investment guarantee in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 297-323, October.
    21. Lin, Shih-Kuei & Lin, Chien-Hsiu & Chuang, Ming-Che & Chou, Chia-Yu, 2014. "A recursive formula for a participating contract embedding a surrender option under regime-switching model with jump risks: Evidence from stock indices," Economic Modelling, Elsevier, vol. 38(C), pages 341-350.
    22. Li, Jing & Szimayer, Alexander, 2010. "The effect of policyholders' rationality on unit-linked life insurance contracts with surrender guarantees," Bonn Econ Discussion Papers 22/2010, University of Bonn, Bonn Graduate School of Economics (BGSE).
    23. Srbinoski Bojan & Strozzi Fernanda & Poposki Klime & Born Patricia H., 2020. "Trends in Life Insurance Demand and Lapse Literature," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 14(2), pages 1-46, July.

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