An extension of Arrow’s result on optimality of a stop loss contract. (English) Zbl 1122.91343

Summary: The optimal, from the cedent’s point of view, reinsurance treaties for a fixed reinsurer’s premium are derived. We assume that the cedent wants to minimize a convex risk measure, e.g. the variance, semi-variance, upper partial moment or mean absolute deviation. The reinsurer’s premium is calculated on the basis of the expectation and variance of his/her part of the total risk. The obtained results provide an extension of Arrow’s result on the optimality of a stop loss treaty.


91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
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