Proportional reinsurance

This thesis deals with the issue of proportional reinsurance. It describes the basic types of proportional reinsurance, Quota Share, Surplus and their modi- fications, Variable Quota Share and Table of Lines Surplus. Furthermore, the paper explains how reinsurance changes aggregate claim amounts in the indivi- dual risk model. In this thesis we introduce two criteria for finding optimal ratio of proportional reinsurance. First, the de Finetti's criterion which minimizes the variance of the result of the insurer subject to a given level for the expected re- sult. Second is the optimality criterion which minimizes the (conditional) value at risk of total costs of the insurance company. Finally, we present numerical examples where on the basis of optimality criteria we find the optimal quota, respectively optimal retention level of the reinsurance.