Stochastic asset allocation and reinsurance strategies for an ambiguity-averse insurer under a generalized contagion risk framework

In this paper, we address an optimal stochastic asset allocation and reinsurance problem in continuous-time contagious financial and insurance markets. The insurer is subject to contagious claims, which are modeled using an enhanced dynamic contagion process. This process generalizes the externally-exciting Cox process with shot noise and the self-exciting Hawkes process while also capturing the dependence structure between the financial and insurance markets. Furthermore, the insurer is assumed to be ambiguity-averse, with distinct modeling risk aversion preferences for the risky asset, extreme external events, and contagious insurance claims. The insurer aims to maximize the expected utility of the terminal surplus and a specified penalty function at a fixed terminal date under the worst-case scenario. Using the dynamic programing principle, we derive the extended Hamilton-Jacobi-Bellman (HJB) equation and develop an iterative numerical scheme to compute the value function and optimal controls. The convergence of the numerical method is rigorously proven. To support our quantitative analysis, we provide several numerical examples illustrating the impact of the dependence structure and ambiguity aversion on optimal controls.