Valuing equity-linked death benefits with a threshold expense strategy

Jiang Zhou and Lan Wu

Insurance: Mathematics and Economics, 2015, vol. 62, issue C, 79-90

Abstract: We investigate equity-linked investment products with a threshold expense strategy, under which an insurance company will collect expenses continuously from the policyholder’s account only when the account value is lower than a pre-specified level. The logarithmic value of the policyholder’s account, before deducting any fees, is described by a jump diffusion process which is independent of the time-to-death random variable. The distribution of the time-to-death random variable is approximated by a combination of exponential distributions, which are dense in the space of density functions on [0,∞). We characterize the Laplace transform of the distribution of a general refracted jump diffusion process through some integro-differential equations. Besides, the distribution of a refracted double exponential jump diffusion process at an independent exponential random variable is derived, from which closed-form formulas to evaluate the total expenses and the fair fee rates are obtained. Finally, we illustrate our results by some numerical examples.

Keywords: Equity-linked products; Guaranteed minimum death benefits; Threshold expense strategy; Refracted Lévy process; Itô’s formula (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:62:y:2015:i:c:p:79-90

DOI: 10.1016/j.insmatheco.2015.03.002

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