Optimal reinsurance under the general mixture risk measures

This paper concerns the problem of how to purchase the reinsurance in order to make the insurer and the reinsurer's total risk least under the standard deviation principle. Sufficient conditions for optimality of reinsurance contract are given within the restricted class of admissible contracts. Here, the insurer and reinsurance company can take arbitrary risk measures, respectively. Further, we give the explicit forms of optimal reinsurance contract under special risk measures. We also give the method to decide the parameters.