Optimally Investing to Reach a Bequest Goal

We determine the optimal strategy for investing in a Black-Scholes market in order to maximize the probability that wealth at death meets a bequest goal $b$. We, thereby, make more objective the goal of maximizing expected utility of death, first considered in a continuous-time framework by Merton (1969). Specifically, instead of requiring the individual to choose a utility function, we only require the individual to choose a bequest goal $b$. We learn that, for wealth lying between $0$ and $b$, the optimal investment strategy is {\it independent} of $b$, a surprising result. Therefore, if the individual were to revise her bequest goal, her investment strategy would not change if her wealth is less than the new goal.