Maximizing a robust goal-reaching probability with penalization on ambiguity

Abstract

This paper studies an optimal robust investment and reinsurance problem for an insurer under a surplus model with ambiguity that the insurer does not have perfect information in drift terms of the risky asset and insurance risk. The ambiguity is described by a set of equivalent measures to a benchmark. The insurer aims to maximize a robust value involving the probability of reaching a high goal before ruin and a penalization of model ambiguity. We characterize the robust value function as the unique classical solution to the Hamilton–Jacobi–Bellman (HJB) equation. We derive the value function in explicit form by solving the HJB equation, and find the optimal investment-reinsurance strategy and drift distortions of the optimal measure in feedback forms. We observe that the optimal strategy under the scenario of ambiguity penalization coincides with the optimal strategy under maximization of the goal-reaching probability in the benchmark case without ambiguity. We further demonstrate the impact of ambiguity-aversion on the insurer’s evaluation and the selection of optimal drift distortions.