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Pricing equity-linked death benefits by complex Fourier series expansion in a regime-switching jump diffusion model

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  • Wang, Yayun
  • Zhang, Zhimin
  • Yu, Wenguang

Abstract

In this paper, we consider the valuation problem of equity-linked annuity with guaranteed minimum death benefit (GMDB) by complex Fourier series method under regime-switching jump diffusion models. We show that the price formulas can be expressed by some discounted density functions associated with the residual lifetime random variable. Fourier transforms for discounted density functions are derived, and complex Fourier series expansion method is applied to recover the discounted density functions. Some explicit formulas for computing the GMDB price are given. Finally, we give some numerical results to show effectiveness of our method.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:399:y:2021:i:c:s0096300321000795
    DOI: 10.1016/j.amc.2021.126031
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    3. David Xiao, 2023. "Valuation of Equity Linked Securities with Guaranteed Return," Papers 2306.15026, arXiv.org.
    4. Yujuan Huang & Jing Li & Hengyu Liu & Wenguang Yu, 2021. "Estimating Ruin Probability in an Insurance Risk Model with Stochastic Premium Income Based on the CFS Method," Mathematics, MDPI, vol. 9(9), pages 1-17, April.
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    6. Deelstra, Griselda & Hieber, Peter, 2023. "Randomization and the valuation of guaranteed minimum death benefits," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1218-1236.
    7. 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.
    8. Lee, David, 2023. "An Analytic Solution for Valuing Guaranteed Equity Securities," MPRA Paper 117775, University Library of Munich, Germany.

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