Analytic solution for ratchet guaranteed minimum death benefit options under a variety of mortality laws

Eric Ulm

Insurance: Mathematics and Economics, 2014, vol. 58, issue C, 14-23

Abstract: We derive a number of analytic results for GMDB ratchet options. Closed form solutions are found for De Moivre’s Law, Constant Force of Mortality, Constant Force of Mortality with an endowment age and constant force of mortality with a cutoff age. We find an infinite series solution for a general mortality laws and we derive the conditions under which this series terminates. We sum this series for at-the-money options under the realistic Makeham’s Law of Mortality.

Keywords: Variable annuities; Laplace transforms; Partial differential equations; Guaranteed minimum death benefits; Closed form solutions (search for similar items in EconPapers)
JEL-codes: G13 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (10)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:58:y:2014:i:c:p:14-23

DOI: 10.1016/j.insmatheco.2014.06.003

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