Robust Non-Zero-Sum Stochastic Differential Investment-Reinsurance Game

This paper considers the non-zero-sum stochastic differential game problem between two ambiguity-averse insurers (AAIs) who encounter model uncertainty and seek the optimal investment and reinsurance decision under relative performance concerns. Each AAI invests in a risky asset and a risk-free asset, and manages her own risks by purchasing reinsurance with the objective of maximizing the expected utility of her relative terminal surplus with respect to that of her counterparty. The two AAIs' decisions influence each other through the insurers' relative performance concerns and the correlation between their surplus processes. We establish a general framework of Nash equilibrium for the associated non-zero-sum game with model uncertainty. For the representative case of exponential utilities and the Heston model, we solve the equilibrium strategies explicitly. Numerical studies are conducted to draw economic interpretations