Optimal investment-reinsurance with delay for mean-variance insurers: a maximum principle approach

This paper is concerned with an optimal investment and reinsurance problem with delay for an insurer under the mean-variance criterion. A three-stage procedure is employed to solve the insurer's mean-variance problem. We first use the maximum principle approach to solve a benchmark problem. Then applying the Lagrangian duality method, we derive the optimal solutions for a variance-minimization problem. Based on these solutions, we finally obtain the efficient strategy and the efficient frontier of the insurer's mean-variance problem. Some numerical examples are also provided to illustrate our results.