The investment and reinsurance game on asset-liability management with common shock dependence under CEV model

This paper investigates the non-zero-sum stochastic differential game problem of optimal asset-liability management (ALM) between insurers and reinsurers. Combining the investment-reinsurance problem with the ALM, this paper innovatively studies the investment-reinsurance ALM non-zero-sum game within the framework of the constant elasticity of variance (CEV) model under common shock dependence. We allow the insurance companies to purchase proportional reinsurance from reinsurance companies, and both companies can invest in a financial market composed of one risk-free asset and one risk asset whose price process follows the CEV model. By innovatively introducing a class of stochastic liability processes associated with the volatility of risky assets, we obtain the dynamic evolution of net wealth. Using stochastic control theory, we obtain an explicit expression of Nash equilibrium strategy for the problem and a closed-form expression for the corresponding equilibrium value function by maximizing the expected utility from the terminal net wealth. Finally, we illustrate the effect of relevant parameters on the optimal investment-reinsurance strategy by means of numerical examples.