OPTIMAL REINSURANCE AND DIVIDEND DISTRIBUTION POLICIES IN THE CRAMÉR‐LUNDBERG MODEL

Abstract

We consider that the reserve of an insurance company follows a Cramér‐Lundberg process. The management has the possibility of controlling the risk by means of reinsurance. Our aim is to find a dynamic choice of both the reinsurance policy and the dividend distribution strategy that maximizes the cumulative expected discounted dividend payouts. We study the usual cases of excess‐of‐loss and proportional reinsurance as well as the family of all possible reinsurance contracts. We characterize the optimal value function as the smallest viscosity solution of the associated Hamilton‐Jacobi‐Bellman equation and we prove that there exists an optimal band strategy. We also describe the optimal value function for small initial reserves.