Special Session 146: 

Investment and Reinsurance Non-Zero-Sum Games with Value-at-Risk Constraints

Zhuo Jin
University of Melbourne
Co-Author(s):    Ning Wang, Nan Zhang, Linyi Qian
This work investigates a class of non-zero-sum stochastic differential investment and reinsurance game between two insurance companies. We assume that both insurers are allowed to purchase a proportional reinsurance and invest in risky and risk-free assets. When applying the generalized variance premium principle in determining reinsurance premium, the surplus process becomes quadratic in the retained proportion of claims. The optimization criterion of each insurer is to maximize his utility of the difference between his terminal surplus and that of his competitor. In addition, we incorporate dynamic VaR constraints to meet the capital requirement from regulators. This game problem can be converted to solving a system of nonlinear equations when we assume both insurers are CARA agents. Finally, we use some numerical examples to illustrate the Nash Equilibrium strategy under different scenarios.