Optimization of risk bearing in a statistical model with reinsurance

The paper is devoted to solving problems of optimal choice of client's risk bearing by the insurer at the level insurer-client and at the level insurer-reinsurer. It was shown that in the model of additional restrictions, the most profitable for the insurer will be the refusal from reinsurance and application of stop-loss insurance strategy. In the problem that takes the restriction on insurer's risk into account, reinsurance of excess of loss and insurance that is a combination of the stop-loss strategy and deductible are optimal. Necessary and sufficient conditions of optimality of parameters of the stated strategies are obtained; an example illustrating the proved results in case of exponential utility functions is given.