STOCHASTIC DIFFERENTIAL GAMES ON INVESTMENT, CONSUMPTION AND PROPORTIONAL REINSURANCE UNDER THE CEV MODEL

In recent years, problems of nonzero-sum investment and reinsurance games have received a lot of attention from scholars. However, for practical consideration, there is also consumption in the operation process of insurers, which is rarely taken into account by scholars. This paper integrated the consumption problem into nonzero-sum investment-reinsurance problems, and studied the nonzero-sum investment, consumption, and reinsurance game between two competitive insurers. Each insurer was allowed to purchase proportional reinsurance and invest in a financial market consisting of a risk-free asset and a risky asset, and the price process of the risky asset was described by the constant elasticity of variance (CEV) model. Moreover, the consumption behavior of each insurer was also considered. The main objective of each insurer was to maximize the utility of his terminal surplus and accumulated consumption relative to that of his competitor. Based on the stochastic differential game theory, we obtained the Hamilton-Jacobi-Bellman (HJB) equations for both insurers and derived the equilibrium strategies and the equilibrium value function. Numerical examples were given in the end to illustrate the influence of model parameters on the equilibrium strategies.