Heterogeneity and the need for capital in the individual model

DOI10.1080/03461230500518690zbMath1142.91039OpenAlexW2034621715MaRDI QIDQ3440845

Michel M. Denuit, Esther Frostig

Publication date: 29 May 2007

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

Full work available at URL: https://doi.org/10.1080/03461230500518690

zbMATH Keywords

stochastic dominancemajorizationconvex orderstop-loss orderLaplace transform orderSchur-increasing functions

Mathematics Subject Classification ID

Related Items (23)

Life anuities with stochastic survival probabilities: A review ⋮ ON HETEROGENEITY IN THE INDIVIDUAL MODEL WITH BOTH DEPENDENT CLAIM OCCURRENCES AND SEVERITIES ⋮ Ordering results for individual risk model with dependent Location-Scale claim severities ⋮ Ordering properties of the smallest and largest claim amounts in a general scale model ⋮ Optimal pricing for a heterogeneous portfolio for a given risk factor and convex distance measure ⋮ Comparison of aggregation, minimum and maximum of two risky portfolios with dependent claims ⋮ Ordering the largest claim amounts and ranges from two sets of heterogeneous portfolios ⋮ Comparisons on aggregate risks from two sets of heterogeneous portfolios ⋮ Ordering results on largest order statistics from multiple-outlier gamma variables ⋮ Stochastic comparisons of the largest claim amounts from two sets of interdependent heterogeneous portfolios ⋮ On stochastic comparison between aggregate claim amounts ⋮ ORDERING PROPERTIES OF EXTREME CLAIM AMOUNTS FROM HETEROGENEOUS PORTFOLIOS ⋮ Stochastic Comparisons between the Extreme Claim Amounts from Two Heterogeneous Portfolios in the Case of Transmuted-G Model ⋮ On the convex transform and right-spread orders of smallest claim amounts ⋮ Ordering Results for Aggregate Claim Amounts from Two Heterogeneous Marshall--Olkin Extended Exponential Portfolios and Their Applications in Insurance Analysis ⋮ Some new results on aggregate claim amounts from two heterogeneous Marshall–Olkin extended exponential portfolios ⋮ Comparisons of aggregate claim numbers and amounts: a study of heterogeneity ⋮ Association and heterogeneity of insured lifetimes in the Lee–Carter framework ⋮ Ranking the extreme claim amounts in dependent individual risk models ⋮ On the increasing convex order of generalized aggregation of dependent random variables ⋮ Stochastic comparisons of the smallest and largest claim amounts with location-scale claim severities ⋮ On transform orders for largest claim amounts ⋮ Stochastic comparison of aggregate claim amounts between two heterogeneous portfolios and its applications

Cites Work

• Optimal reinsurance and stop-loss order
• Some recent developments on majorization inequalities in probability and statistics
• Laplace transform ordering of actuarial quantities.
• Analysis of heterogeneous endowment policies portfolios under fractional approximations.
• Insurance contracts portfolios with heterogeneous insured ages
• Monotonicity results for portfolios with heterogeneous claims arrival processes
• Insurance contracts portfolios with heterogenous parametric life distributions
• Life Insurance Policies with Statistical Heterogeneous Population
• A Universal Framework for Pricing Financial and Insurance Risks
• The Dual Theory of Choice under Risk
• Inequalities: theory of majorization and its applications

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