Study Of Optimal Reinsurance Under The Re-insurer's Risk Constraints

This thesis introduces and discusses the optimal reinsurance under the risk constraints of the reinsurer.First we has described the reinsurance basic concept, the classification as well as the reinsurance premium criterion, introduced ele-mentary knowledge related to reinsurance such as guidelines for expected utility and risk attitudes, etc. Then we have summarized the optimal reinsurance re-search achievements on the basis of the expected utility theory, and for further discussion. In practice, in order to control risk, the reinsurer require that the risk limits covered can not be too large, and the average risk not too high. This thesis taking into account the original insurer and the reinsurer's common interests, un-der the condition of the reinsurer assigning the risk constraints, we discuss that how to obtain the optimal reinsurance strategies which maximize the original insurer's expected utility.Here in this thesis we add two risk constraints of the reinsurer in the basis of Arrow's model, one is the limit of reinsurer's risk, the other is the limit of reinsurer's claims in excess of the mean premium. On this basis, we establish the corresponding mathematical model, and discussed and analysis the model in detail,the conclusion is: the second constraint of the optimal reinsurance model can be divided into two kinds of cases, namely binding and not binding, In both cases the optimal solution is the piecewise linear function of the risk X, just in a different form; Moreover, the original insurer's expected utility will increase if the reinsurer increase his risk tolerances.In the end, this thesis gives out two specific forms of the optimal solution of the optimal reinsurance model and solution methods, then explained it in detail through example that the insurer's utility function of wealth is assumed to be the exponential function.