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Article

# Valuing Guaranteed Minimum Death Benefits by Cosine Series Expansion

by 1,*, 3,*, 2 and
1
School of Insurance, Shandong University of Finance and Economics, Jinan 250014, China
2
College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
3
School of Science, Shandong Jiaotong University, Jinan 250357, China
4
School of Computer Science & Technology, Shandong University of Finance and Economics, Jinan 250014, China
*
Authors to whom correspondence should be addressed.
Mathematics 2019, 7(9), 835; https://doi.org/10.3390/math7090835
Received: 2 August 2019 / Revised: 4 September 2019 / Accepted: 5 September 2019 / Published: 10 September 2019
(This article belongs to the Special Issue Stochastic Processes: Theory and Applications)
Recently, the valuation of variable annuity products has become a hot topic in actuarial science. In this paper, we use the Fourier cosine series expansion (COS) method to value the guaranteed minimum death benefit (GMDB) products. We first express the value of GMDB by the discounted density function approach, then we use the COS method to approximate the valuation Equations. When the distribution of the time-until-death random variable is approximated by a combination of exponential distributions and the price of the fund is modeled by an exponential Lévy process, explicit equations for the cosine coefficients are given. Some numerical experiments are also made to illustrate the efficiency of our method. View Full-Text
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MDPI and ACS Style

Yu, W.; Yong, Y.; Guan, G.; Huang, Y.; Su, W.; Cui, C. Valuing Guaranteed Minimum Death Benefits by Cosine Series Expansion. Mathematics 2019, 7, 835. https://doi.org/10.3390/math7090835

AMA Style

Yu W, Yong Y, Guan G, Huang Y, Su W, Cui C. Valuing Guaranteed Minimum Death Benefits by Cosine Series Expansion. Mathematics. 2019; 7(9):835. https://doi.org/10.3390/math7090835

Chicago/Turabian Style

Yu, Wenguang, Yaodi Yong, Guofeng Guan, Yujuan Huang, Wen Su, and Chaoran Cui. 2019. "Valuing Guaranteed Minimum Death Benefits by Cosine Series Expansion" Mathematics 7, no. 9: 835. https://doi.org/10.3390/math7090835

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