On the free boundary of an annuity purchase

Tiziano De Angelis and Gabriele Stabile

Papers from arXiv.org

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 if 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 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 non-monotonic optimal boundaries.

Date: 2017-07, Revised 2018-07
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Journal Article: On the free boundary of an annuity purchase (2019)
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