On the free boundary of an annuity purchase

TL;DR

This paper investigates the optimal timing for annuity purchase considering time-varying mortality rates and subjective life expectancy, using a real options approach and developing new methods for non-monotonic stopping boundaries.

Contribution

It introduces a novel probabilistic framework for optimal annuity purchase with time-dependent mortality, addressing non-monotonic boundaries and subjective vs. objective life expectancy.

Findings

Derived new solution methods for non-monotonic stopping boundaries.

Analyzed the impact of subjective life expectancy on optimal purchase timing.

Provided detailed characterization of the optimal stopping boundary.

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.