Risk Measures Induced by Efficient Insurance Contracts

The Expected Shortfall (ES) is one of the most important regulatory risk measures in finance, insurance, and statistics, which has recently been characterized via sets axioms from perspectives portfolio management statistics. Meanwhile, there large literature on insurance design with ES as an objective or a constraint. A visible gap to justify special role actuarial science. To fill this gap, we study characterization induced by efficient contracts, i.e., those that are Pareto optimal for insured insurer. One our major results characterize mixture mean measure insurer, when contracts deductibles efficient. Characterization other measures, including distortion also presented linking them different contracts.