Minimizing the Probability of Lifetime Ruin When Shocks Might Occur: Perturbation Analysis

We determine the optimal investment strategy to minimize the probability of an individual’s lifetime ruin when the underlying model parameters are subject to a shock. Specifically, we consider two possibilities: (1) changes in the individual’s net consumption and mortality rate and (2) changes in the parameters of the financial market. We assume that these rates might change once at a random time. Changes in an individual’s net consumption and mortality rate occur when the individual experiences an accident or other unexpected life event, while changes in the financial market occur due to shifts in the economy or in the political climate. We apply perturbation analysis to approximate the probability of lifetime ruin and the corresponding optimal investment strategy for small changes in the model parameters and observe numerically that these approximations are reasonable ones, even when the changes are not small.