Scandinavian Actuarial Journal · 1983 · 12 citations · 5 references
BusinessFinanceMathematicsActuarial ScienceFinancial EconomicsInsurance EconomicsIntegral EquationsLinear ProgrammingLoss Distribution AnalysisOptimization TheoryProbability InequalitiesRisk TheoryConstraintsDual Linear ProgrammingDuality TheoryLoss Distribution TheoryMinimax RiskRetention Limit DeterminationRiskStop-loss Pricing
Abstract We consider the problem of maximization (or minimization) of an integral ∫fdF under various constraints on the distribution F. The problem is practically equivalent to a dual linear problem with an infinite number of constraints. The theory is applied to the determination of sharp bounds on the stop-loss premium E(X −t)+ corresponding to the risk X and the retention limit t, in case of incomplete information on the distribution F of X. Several new types of constraints, not yet considered in the actuarial literature, are developed.
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