A Reinsurance Approach in a Two-Dimensional Model with Dependent Risks

We consider an insurer having two classes of insurance risks dependent through the number of claims of each risk in a given period of time. We assume that the insurer chooses a reinsurance strategy related to the first class of risk by means a proportional reinsurance contract; we also assume that the reinsurance strategy related to the second class of risk is of Excess of Loss reinsurance type. Within this paper, we study the possible optimal couples of proportional retention level and Excess of Loss retention limit.