Non-zero-sum investment-reinsurance game with delay and ambiguity aversion

Abstract

In this paper, we investigate a investment-reinsurance game problem with delay and ambiguity aversion for two insurers under mean–variance preference. Each insurer can purchase proportional reinsurance whose surplus process is a diffusion approximation process, and invest oneself’s wealth in a financial market consisting of a risk-free asset and a risky asset whose price evolution follows a jump–diffusion process. Based on the introduction of delay, we obtain wealth dynamics for each insurer depicted by a stochastic delay differential equation. By the stochastic control theory in the framework of game theory, the robust time-consistent Nash equilibrium investment-reinsurance strategies and the corresponding robust equilibrium value functions for each insurer are derived. Furthermore, some numerical examples are provided to illustrate the effect of market parameters on the optimal investment-reinsurance strategy.