Lorenz and Excess Wealth Orders, with Applications in Reinsurance Theory

DOI10.1080/03461239950132642zbMath0952.91041OpenAlexW2120661795MaRDI QIDQ4512140

Catherine Vermandele, Michel M. Denuit

Publication date: 1 November 2000

Published in: Scandinavian Actuarial Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03461239950132642

zbMATH Keywords

Lorenz orderoptimal reinsurancestochastic dominanceconvex orderdispersive orderstop-loss orderArrow-Ohlin theoremVajda-Ohlin theoremexcess wealthorder loss ratios

Mathematics Subject Classification ID

Related Items (14)

ORDERING RESULTS ON EXTREMES OF EXPONENTIATED LOCATION-SCALE MODELS ⋮ Ordering Gini indexes of multivariate elliptical risks ⋮ Some results for the comparison of generalized order statistics in the total time on test and excess wealth orders ⋮ Optimal retention for a stop-loss reinsurance with incomplete information ⋮ On the second-order excess wealth order and its properties ⋮ Optimal reinsurance with positively dependent risks ⋮ Convex order and comonotonic conditional mean risk sharing ⋮ Comparing tail variabilities of risks by means of the excess wealth order ⋮ Stochastic comparisons of imperfect maintenance models for a gamma deteriorating system ⋮ Characterization of higher-degree dispersion, right spread and stop-loss transform orders ⋮ Stochastic comparisons of distorted variability measures ⋮ On sufficient conditions for the comparison in the excess wealth order and spacings ⋮ Comparison of risks based on the expected proportional shortfall ⋮ Analytic expressions for multivariate Lorenz surfaces

Cites Work

• Unnamed Item
• Phase-type distributions and majorization
• Dispersive ordering by the spread function
• Ordering of risks: a review
• Increases in risk and deductible insurance
• Orderings of risks through loss ratio
• Optimal reinsurance and stop-loss order
• Extensions of Ohlin's lemma with applications to optimal reinsurance structures
• Lorenz ordering of power-function order statistics
• Some new classes of stochastic order relations among arithmetic random variables, with applications in actuarial sciences
• Optimal reinsurance in relation to ordering of risks
• Ordering claim size distributions and mixed Poisson probabilities
• Optimal insurance without expected utility: The dual theory and the linearity of insurance contracts
• Orderings of risks: A comparative study via stop-loss transforms
• The utility of deductibles from the insurer's point of view
• Convex majorization with an application to the length of critical paths
• Choosing Between Risky Prospects: The Characterization of Comparative Statics Results, and Location Independent Risk
• The Generating Process and an Extension of Jewitt's Location Independent Risk Concept
• Two Variability Orders

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