Robust optimal investment and reinsurance to minimize a goal-reaching probability with constrained control variables

Abstract

This paper considers a robust optimal investment and reinsurance problem with constraints for an Ambiguity-Averse Insurer (AAI). The criterion is to minimize the goal-reaching probability, namely, the probability that the value of the wealth process reaches a low barrier before a high goal. The robust optimal investment-reinsurance strategy and closed-form expression of the associated value function are derived explicitly by applying stochastic dynamic programming and solving the corresponding Hamiliton-Jacobi-Bellman (HJB) equation. It is extremely interesting that the sum of our value function and the value function of Luo et al. [23] is equal to 1 in two cases of ambiguity and ambiguity-neutral. Finally, numerical examples are given to illustrate the influence of typical parameters on our results.