On the free boundary of an annuity purchase

Tiziano Angelis () and Gabriele Stabile
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Tiziano Angelis: University of Leeds

Finance and Stochastics, 2019, vol. 23, issue 1, No 3, 97-137

Abstract: Abstract It is known that the decision to purchase an annuity may be associated to an optimal stopping problem. However, little is known about optimal strategies if the mortality force is a generic function of time and the subjective life expectancy of the investor differs from the objective one adopted by insurance companies to price annuities. In this paper, we address this problem by considering an individual who invests in a fund and has the option to convert the fund’s value into an annuity at any time. We formulate the problem as a real option and perform a detailed probabilistic study of the optimal stopping boundary. Due to the generic time-dependence of the mortality force, our optimal stopping problem requires new solution methods to deal with nonmonotonic optimal boundaries.

Keywords: Annuities; Mortality force; Optimal stopping; Free boundary problems; 91G80; 62P05; 60G40; 35R35 (search for similar items in EconPapers)
JEL-codes: J26 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (10)

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Working Paper: On the free boundary of an annuity purchase (2018)
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DOI: 10.1007/s00780-018-00379-8

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