OptimalreinsuranceundertheExpectedShortfall(ES)riskmeasureisakeytopicinactuarialscienceandriskmanagement.ExpectedShortfall,alsoknownasConditionalValue-at-Risk(CVaR),measurestheaveragelossbeyondaspecifiedconfidencelevel,providingamorecomprehensiveriskassessmentthanValue-at-Risk(VaR).Inthiscontext,optimalreinsuranceaimstodesigncontractsthatminimizetheinsurer'sriskexposure,quantifiedbyES,whileconsideringreinsurancecostsandotherconstraints.Commonreinsuranceformsincludeproportional(quota-share)andnon-proportional(excess-of-loss,stop-loss)treaties.Researchinthisareaexploreshowdifferentreinsurancestructuresaffecttheinsurer'sriskprofileunderES,oftenusingoptimizationtechniquesandstochasticmodeling.Thefindingshelpinsurersbalancerisktransferandprofitability,ensuringsolvencyandregulatorycompliance.Keychallengesincludeincorporatingdependenceamongrisks,optimizingmulti-periodreinsurancestrategies,andaligningreinsurancedecisionswithcapitalrequirementsunderframeworkslikeSolvencyII.Advancesinthisfieldcontributetomorerobustriskmanagementpracticesintheinsuranceindustry.
