Abstract: An optimal investment and reinsurance problem for insurers under mean-variance criterion was investigated, whose surplus process is described by a more general jump-diffusion process and aims to seek the corresponding time-consistent strategy. The financial market consists of one risk-free asset and multiple risky assets whose price processes follow geometric Levy processes. The closed-form expressions for the time-consistent investment and reinsurance strategies and the optimal value function were derived by solving an extended Hamilton-Jacobi-Bellman equation.

Key words: investment and reinsurance, multiple risky assets, extended Hamilton-Jacobi-Bellman equation, time-consistent strategy, mean-variance criterion