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Optimal reinsurance with general risk measures. (English) Zbl 1162.91394
Summary: This paper studies the optimal reinsurance problem when risk is measured by a general risk measure. 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. The paper ends by particularizing the findings, so as to study in detail two deviation measures and the conditional value at risk.

MSC:
91B30 Risk theory, insurance (MSC2010)
91B28 Finance etc. (MSC2000)
90C48 Programming in abstract spaces
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