Abstract: We considered a Stackelberg stochastic differential game problem with an ambiguity-averse reinsurance company as the leader and an ambiguity-neutral insurance company  as the follower. By solving the extended HJB (Hamilton-Jacobi-Bellman) equation systems, we gave the robust optimal investment-reinsurance strategies and the corresponding value function under the time-consistent mean-variance criterion. Finally, we gave some numerical examples and sensitivity analyses to illustrate the relationship between the optimal strategies and the main parameters.

Key words: proportion reinsurance, constant , coefficient variance elasticity model, Stackelberg differential game, time-consistent mean-variance framework,  , ambiguity aversion