Valuing guaranteed equity-linked contracts under piecewise constant forces of mortality

Xiaoqing Liang, Cary Chi-Liang Tsai and Yi Lu

Insurance: Mathematics and Economics, 2016, vol. 70, issue C, 150-161

Abstract: The work of this paper is motivated by the study in Gerber et al. (2012) and some following papers, in which equity-linked death benefits embedded in various variable annuity products are valuated for any time-until-death random variables whose density function can be approximated by a linear combination of densities of exponential random variables. Their analysis is made for the case where the time-until-death is exponentially distributed, i.e., under the assumption of a constant force of mortality. The main purpose of our study is to show that the discounted density approach can also be used to obtain similar explicit results on life-contingent options under the assumption of piecewise constant forces of mortality. Moreover, we study a term insurance product with the payoff at the time of death being equity-linked and inflation-indexed, and investigate two types of annuity-immediate products whose annual payments are equity-indexed with a minimum guaranteed amount. We also illustrate approximations and numerical calculations for some results obtained in this paper, and analyze parameter sensitivities.

Keywords: Equity-linked death benefits; Minimum guaranteed death benefits; Life-contingent options; Piecewise constant forces of mortality; Variable annuities; Inflation-indexed death benefits; Guaranteed variable annuities (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:70:y:2016:i:c:p:150-161

DOI: 10.1016/j.insmatheco.2016.06.004

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