Abstract
This paper concerns how to purchase the reinsurance to minimize both the insurer and the reinsurers risk fluctuation under the standard deviation principle. Sufficient conditions for the optimal reinsurance contract are obtained in the restricted class of admissible contracts. Assume that the reinsurers risk is less than a threshold, and then wefind out the optimal reinsurance contract that minimizes the insurers risk. Here the insurer company can take three general and useful risk measures.
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