Optimal Reinsurance-Investment Game for Two Insurers with Sahara Utilities Under Correlated Markets

The number of insurance companies recently have increased dramatically, some insurance businesses of insurance companies tend to be the same, but their wealth and risk preference are different. Therefore, this paper studies the reinsurance investment game between insurers with the same insurance business but different wealth and risk preferences. Assume that the insurers who have the symmetric asymptotic hyperbolic absolute risk aversion (SAHARA) utilities and can participate the reinsurance market and a risk related financial market consisting of a risk-free asset and a risky asset whose price process obeys the constant elasticity of variance (CEV) model. It is not possible to get closed form solution due to the non-homothetic property and there is little literature on the numerical scheme to solve the HJB equation with CEV model for SAHARA utilities. We establish a strong duality relationship of the value function, and propose an efficient dual control Monte Carlo method for computing the Nash equilibrium strategies. Finally, numerical analysis is presented to illustrate the impact of model parameters Nash equilibrium strategies