Study Of Optimal Reinsurance Under General Risk Measures

This paper introduces and discusses the optimal reinsurance problem when risk is measured by a general risk measure. First we has described the reinsurance basic concept, including the kinds of reinsurance strategy and premium calculation principles, etc. Then we have summarized the optimal reinsurance research achievements on general risk measures and premium principles. The core part mainly discusses the optimal reinsurance strategy under the expectation calculation. To prove whether general type reinsurance has met the optimality conditions, particularly in the quota-share reinsurance and stop-loss reinsurance contract as an example to illustrate the conclusions.This paper considers that the reinsurer's premium principle is given by a convex function, and deal with the optimal reinsurance problem if risk is measured by modern risk measures. Necessary and sufficient optimality conditions are given for a wide family of risk measures, including deviation measures, expectation bounded risk measures and coherent measures of risk. The optimality conditions are used to verify whether the classical reinsurance contracts (quota-share, stop-loss) are optimal essentially, regardless of the risk measure used. Thus a unified approach is developed that essentially does not depend on the concrete risk measure to be used.In the end, this paper studies two deviation measures and the conditional value at risk, and takes the special risk function as an example in detail.