Optimal Mean-variance Reinsurance With Dependent Risks

In this thesis, we consider the optimal proportional reinsurance problem for an insurer with two dependent classes of insurance business, where the two claim number processes are correlated through a commom shock component. By the technique of stochastic linear-quadratic control theory and Hamilton-Jacobi-Bellman equation, we derive the explicit expressions of the optimal reinsurance strategies and value function, and present the verification theorem within the framework of the viscosity solution. Furthermore, we extend the results in the linear-quadratic setting to the mean-variance problem, and obtain the efficient strategy and efficient frontier. Some numerical examples are given to show the impact of model parameters on the efficient frontier.