Optimal time-consistent reinsurance-investment strategies for mean-variance insurers with delay

In this work, we study the equilibrium investment-reinsurance /new business and investment strategy for mean-variance insurers with state dependent risk aversion, the insurers are allowed to purchase proportional reinsurance, acquire new business and invest in a financial market, where both the surplus and the price process of risky stocks of the insurers are assumed to follow geometric Levy process. Under the consederation of the performance related capital inflow/outflow, the wealth process of the investor is modeled by a stochastic differential delay equation (SDDE) with jumps. The insurers aim to optimize the mean-variance utility of the combination of terminal wealth and average performance wealth. We formulate the optimal investment and reinsurance mean-variance problem within a game theoretic framework, seeking subgame perfect Nash equilibrium then applying the stochastic control theory with delay.