Optimal timing for annuitization, based on jump diffusion fund and stochastic mortality

Optimal timing for annuitization is developed along three approaches. Firstly, the mutual fund in which the individual invests before annuitization is modeled by a jump diffusion process. Secondly, instead of maximizing an economic utility, the stopping time is used to maximize the market value of future cash-flows. Thirdly, a solution is proposed in terms of Expected Present Value operators: this shows that the non-annuitization (or continuation) region is either delimited by a lower or upper boundary, in the domain time-assets return. The necessary conditions are given under which these mutually exclusive boundaries exist. Further, a method is proposed to compute the probability of annuitization. Finally, a case study is presented where the mutual fund is fitted to the S&P500 and mortality is modeled by a Gompertz Makeham law with several real scenarios being discussed.