STOCHASTIC DIFFERENTIAL INVESTMENT AND REINSURANCE GAME BETWEEN AN INSURER AND A REINSURER WITH DELAY AND DEFAULT RISK UNDER THINNING DEPENDENCE STRUCTURE

. This paper investigates a stochastic differential investment and reinsurance game between an insurer and a reinsurer with delay and default risk. The insurer has the option to purchase a proportional reinsurance contract to mitigate claim risk while investing in three assets: a risk-free asset, a risky asset whose price process is described by the square-root factor model, and a defaultable bond. The reinsurer can sell reinsurance contracts and invest in the financial market. Furthermore, the claim business between the insurer and the reinsurer is correlated through the thinning dependence structure. In consideration of the performance-related capital inflow/outflow, the wealth process of the insurer or reinsurer is modeled by a stochastic differential delay equation. The competitive relationship between them is characterized by the non-zero-sum stochastic differential game in which they consider the relative performance measured by the difference in their terminal wealth. The objective of each competitor is to maximize the mean-variance utility of the combination of his terminal wealth and the relative performance. Subsequently, we solve the extended Hamilton-Jacobi-Bellman equation and then the Nash equilibrium strategies as well as the value functions are derived. Finally, sensitivity analysis is conducted to explain the effects of model parameters on the equilibrium strategy.