Optimal Risk Control and Dividend Distribution Policies. Example of Excess-of Loss Reinsurance for Insurance Corporation

We consider a model of a nancial corporation which has to nd an optimal policy balancing its risk and expected proots. The example treated in this paper is related to an insurance company with the risk control method known in the industry as excess-of-loss reinsurance. Under this scheme the insurance company divert part of its premium stream to another company in exchange of an obligation to pick up that amount of each claim which exceeds a certain level a, This reduces the risk but it also reduces the potential proot. The objective is to make a dynamic choice of a and nd the dividend distribution policy, which maximizes the cumulative expected discounted dividend pay-outs. We use diiusion approximation for this optimal control problem. Mathematical it becomes a mixed singular-regular control problem for diiusion processes. Its analytical part is related to a free boundary (Stephan) problem for a linear second order diierential equation.