Optimal annuitization and bequest motives

Timing the annuitization decision has important economic implications because it has a direct effect on how well prepared individuals are to provide consumptions in their old age. It depends on several risk factors such as market risk, longevity risk, potential future needs of liquid fund and bequest motives. Since the seminal contribution of Yaari (1965), who showed that individuals with no bequest motive should convert all their retirement wealth into annuities, a number of papers have analysed the annuitization decision under the so-called all or nothing institutional arrangement, where immediate lifetime annuities are purchased just at a one point in time. In this paper we investigate the effect of bequest motivesontheannuitizationdecisionforaretiredindividualwhomaximizesthemarketvalue of future cash-flows. From a mathematical point of view the problem is formulated as an optimalstoppingproblem. Byusingthegeometricapproachtooptimalstoppingproblemfor one-dimensional diffusion developed by Dayanik and Karatzas in [6], we determine explicitly the value function as well as the optimal stopping time. Finally, we present numerical examples comparing the optimal annuitization time with and without bequest motives.