Optimal reinsurance under general risk measures

The paper concerns the problem of purchasing the best risk protection from a reinsurance company. The question of choosing the risk measure is discussed and several choices of nonsymmetric risk measures are examined. Sufficient conditions for optimality of a reinsurance contract are given for arbitrary risk measure within any restricted class of admissible contracts. Explicit forms of optimal contracts are derived in the case of absolute deviation and truncated variance risk measures.