Time-consistent reinsurance-investment strategy for mean-variance insurers with defaultable security and jumps

This paper studies an optimal reinsurance-investment problem for a mean-variance insurer with defaultable security and jumps. Specially, we assume that the risky asset`s price process is described by a geometric Lévy process. By using a game theoretic approach, we establish the extended Hamilton-Jacobi-Bellman system for the post-default case and the pre-default case, respectively. Furthermore, we derive the closed-from expressions for the time-consistent reinsurance-investment strategy and the corresponding value function. Finally, we provide numerical examples to illustrate the impacts of model parameters on the time-consistent strategy.