On Penalized Goal-Reaching Probability Minimization with a Common Shock for an AAI

The authors consider a robust optimal reinsurance and investment problem in a risk model with two dependent classes of insurance business for an Ambiguity-Averse insurer (AAI). The insurer aims to minimize the goal-reaching probability that the value of the wealth process reaches a low barrier before a high goal. Using the stochastic control approach based on the Hamilton-Jacobi-Bellman (HJB) equation, the authors derive the robust optimal reinsurance and investment strategies, as well as the corresponding value function. The authors conclude that the robust optimal investment-reinsurance strategy coincides with the one without model ambiguity, but the value function differs. As a consequence, ignoring model uncertainty leads to significant value function loss for the AAI. Besides, it is worth noting that if the insurer has only one business, the sum of the degenerated value function and the one of (Luo, et al., 2019) is equal to 1 both for ambiguity and ambiguity-neutral. Finally, numerical examples are given to illustrate our results.