Lifetime ruin under ambiguous hazard rate

We determine the optimal robust investment strategy of an individual who targets a given rate of consumption and who seeks to minimize the probability of lifetime ruin when her hazard rate of mortality is ambiguous. By using stochastic control, we characterize the value function as the unique classical solution of an associated Hamilton-Jacobi-Bellman equation, obtain feedback forms for the optimal strategies for investing in the risky asset and distorting the hazard rate, and determine their dependence on various model parameters. We also include numerical examples to illustrate our results, as well as perturbation analysis for small values of the parameter that measures one's level of ambiguity aversion.