Distributionally Robust Goal-Reaching Optimization in the Presence of Background Risk

In this article, we examine the effect of background risk on portfolio selection and optimal reinsurance design under criterion maximizing probability reaching a goal. Following literature, adopt dependence uncertainty to model ambiguity between financial (or insurable risk) risk. Because goal-reaching objective function is nonconcave, these two problems bring highly unconventional challenging issues for which classical optimization techniques often fail. Using quantile formulation method, derive solutions explicitly. The results show that presence does not alter shape solution but instead changes parameter value solution. Finally, numerical examples are given illustrate verify robustness our solutions.