چكيده لاتين :
In risk theory , individual risks are usually assumed to be independent, because their mathematical analysis is easier. The importance of modeling dependent risks have been emphasized by specialists. Their intention is to improve the existing tools and models and add to the accuracy of the estimates of accumulated loss for portfolios of insurance risks. Modeling dependent risks has close connections to dynamic financial analysis. In this research, from the insurance point of view, the optimal excess of loss retention limits for two dependent risks has an important role.
We consider two optimization criteria, which are quite connected. We consider that the number of claims is generated by a bivariate poisson distribution. The first function is expected utility of wealth with respect to the exponential utility function that insurer achieves the optimum resolvent by maximizing it to loss retention and the second one is adjustment coefficient of the retained aggregate claims amount that we achieve retention by maximizing this function. Although the systems of equations, that give the optimal solution for both problems, look quite similar, we will see that the optimal solution is completly dependent on the criterion chosen.
