  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.
