Optimal Time-consistent Investment And Reinsurance Strategies For Mean-variance Insurer

Stochastic optimal control or dynamic programming method is a powerful tool to solve many dynamic optimization problems in the finance and economics.With the finance and economics theory are unceasingly rich and the development,a lot of time-inconsistent stochastic control problems appears.Therefore,we cannot use dynamic programming standard method to solve this problem.The optimal solution of the traditional mean-variance problem is only the optimal solution at the initial time.It has time inconsistency.In this paper,we will take into account the correlation of insurance risks and the time inconsistency of strategy.We study the optimal investment-reinsurance problem under the criterion of mean-variance in a risk model with two dependent classes of insurance business.However,it is a well-known fact that the mean-variance criterion lacks the iterated-expectation property.As a result,stochastic control problem for mean-variance criterion is time-inconsistent.we aim to seek the corresponding time-consistent strategies using the time-inconsistent stochastic control theoretic,Bj ¨ork and Murgoci studied.By solving an extended Hamilton-Jacobi-Bellman system,the closed-form expressions of the optimal time-consistent investmentreinsurance strategies and the optimal value function are derived.Finally,some numerical illustrations are presented to show the impact of model parameters on the optimal time-consistent strategies.