Equilibrium reinsurance-investment strategies with partial information and common shock dependence

In this paper, we study an optimal reinsurance-investment problem with partial information and common shock dependence under the mean-variance criterion for an insurer. The insurer has two dependent classes of insurance business, which are subject to a common shock. We consider the optimal reinsurance-investment problem under complete information and partial information, respectively. We formulate the complete information problem within a game theoretic framework and seek the equilibrium reinsurance-investment strategy and equilibrium value function by solving an extended Hamilton-Jacobi-Bellman system of equations. For the partial information problem, we first transform it to a completely observable model by virtue of the filtering theory, then derive the equilibrium strategy and equilibrium value function by using the methods similar to those for the complete information problem. In addition, we illustrate the equilibrium reinsurance-investment strategies by numerical examples and discuss the impacts of model parameters on the equilibrium reinsurance-investment strategies for both the complete information and partial information cases.