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Valuing Equity‐Linked Death Benefits on Multiple Life with Time until Death following a Kn Distribution

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  • Franck Adékambi
  • Essomanda Konzou

Abstract

The purpose of this paper is to investigate the valuation of equity‐linked death benefit contracts and the multiple life insurance on two heads based on a joint survival model. Using the exponential Wiener process assumption for the stock price process and a Kn distribution for the time until death, we provide explicit formulas for the expectation of the discounted payment of the guaranteed minimum death benefit products, and we derive closed expressions for some options and numerical illustrations. We investigate multiple life insurance based on a joint survival using the bivariate Sarmanov distribution with Kn (i.e., the Laplace transform of their density function is a ratio of two polynomials of degree at most) marginal distributions. We present analytical results of the joint‐life status.

Suggested Citation

  • Franck Adékambi & Essomanda Konzou, 2023. "Valuing Equity‐Linked Death Benefits on Multiple Life with Time until Death following a Kn Distribution," Journal of Applied Mathematics, John Wiley & Sons, vol. 2023(1).
    • Handle: RePEc:wly:jnljam:v:2023:y:2023:i:1:n:9984786
    DOI: 10.1155/2023/9984786
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    References listed on IDEAS

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    1. Søren Asmussen & Patrick J. Laub & Hailiang Yang, 2019. "Phase-Type Models in Life Insurance: Fitting and Valuation of Equity-Linked Benefits," Risks, MDPI, vol. 7(1), pages 1-22, February.
    2. 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.
    3. Monique Jeanblanc & Marc Yor & Marc Chesney, 2009. "Mathematical Methods for Financial Markets," Springer Finance, Springer, number 978-1-84628-737-4, March.
    4. 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.
    5. X. Lin & Xiaoming Liu, 2007. "Markov Aging Process and Phase-Type Law of Mortality," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(4), pages 92-109.
    6. Kokou Essiomle & Franck Adékambi, 2023. "Valuation of Equity-Linked Death Benefits on Two Lives with Dependence," Risks, MDPI, vol. 11(1), pages 1-26, January.
    7. 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).
    8. Dhaene, Jan & Stassen, Ben & Barigou, Karim & Linders, Daniël & Chen, Ze, 2017. "Fair valuation of insurance liabilities: Merging actuarial judgement and market-consistency," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 14-27.
    9. 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.
    10. Siu, Chi Chung & Yam, Sheung Chi Phillip & Yang, Hailiang, 2015. "Valuing Equity-Linked Death Benefits In A Regime-Switching Framework," ASTIN Bulletin, Cambridge University Press, vol. 45(2), pages 355-395, May.
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