Multivariate skew-normal distributions with applications in insurance

DOI10.1016/j.insmatheco.2005.11.001zbMath1132.91501OpenAlexW2007332462MaRDI QIDQ2492184

Raluca Vernic

Publication date: 9 June 2006

Published in: Insurance Mathematics \& Economics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.insmatheco.2005.11.001

zbMATH Keywords

multivariate skew-normal distributioncapital allocationtail conditional expectation

Mathematics Subject Classification ID

Related Items (46)

Fitting insurance and economic data with outliers: a flexible approach based on finite mixtures of contaminated gamma distributions ⋮ Extremal properties of the skew-\(t\) distribution ⋮ Data breaches: goodness of fit, pricing, and risk measurement ⋮ Evaluating Risk Measures Using the Normal Mean-Variance Birnbaum-Saunders Distribution ⋮ A derivation of the multivariate singular skew-normal density function ⋮ Remarks for the singular multivariate skew-normal distribution and its quadratic forms ⋮ A Note On Regions of Given Probability of the Extended Skew-normal Distribution ⋮ Multiplicative background risk models: setting a course for the idiosyncratic risk factors distributed phase-type ⋮ Compound unimodal distributions for insurance losses ⋮ Necessary sample sizes for specified closeness and confidence of matched data under the skew normal setting ⋮ Can a regulatory risk measure induce profit-maximizing risk capital allocations? The case of conditional tail expectation ⋮ Modeling right-skewed financial data streams: a likelihood inference based on the generalized Birnbaum-Saunders mixture model ⋮ Asymptotic results on marginal expected shortfalls for dependent risks ⋮ Conditional tail risk measures for the skewed generalised hyperbolic family ⋮ Tail risk measures and risk allocation for the class of multivariate normal mean-variance mixture distributions ⋮ Multivariate tail conditional expectation for scale mixtures of skew-normal distribution ⋮ Tail conditional expectation for multivariate distributions: a game theory approach ⋮ Skew-elliptical distributions with applications in risk theory ⋮ Dependence modelling in insurance via copulas with skewed generalised hyperbolic marginals ⋮ Portfolio separation properties of the skew-elliptical distributions, with generalizations ⋮ Asymptotics for risk capital allocations based on conditional tail expectation ⋮ Multivariate Tweedie distributions and some related capital-at-risk analyses ⋮ Hessian and increasing-Hessian orderings of scale-shape mixtures of multivariate skew-normal distributions and applications ⋮ Weighted risk capital allocations in the presence of systematic risk ⋮ On generalized log-Moyal distribution: a new heavy tailed size distribution ⋮ On the independence of singular multivariate skew-normal sub-vectors ⋮ An alternative matrix skew-normal random matrix and some properties ⋮ Moment matching approximation of Asian basket option prices ⋮ Weighted risk capital allocations ⋮ A stochastic ordering based on the canonical transformation of skew-normal vectors ⋮ Tail dependence and heavy tailedness in extreme risks ⋮ Fitting asset returns to skewed distributions: are the skew-normal and skew-Student good models? ⋮ Skewed bivariate models and nonparametric estimation for the CTE risk measure ⋮ Goodness-of-fit test for tail copulas modeled by elliptical copulas ⋮ Skew generalized extreme value distribution: Probability-weighted moments estimation and application to block maxima procedure ⋮ A Reconciliation of the Top-Down and Bottom-Up Approaches to Risk Capital Allocations: Proportional Allocations Revisited ⋮ Tail conditional risk measures for location-scale mixture of elliptical distributions ⋮ Development of statistical convolutions of truncated normal and truncated skew normal distributions with applications ⋮ Pooling Risk Games ⋮ Lower convex order bound approximations for sums of log-skew normal random variables ⋮ MULTIVARIATE DISTRIBUTIONS WITH TIME AND CROSS-DEPENDENCE: AGGREGATION AND CAPITAL ALLOCATION ⋮ A new family of heavy tailed distributions with an application to the heavy tailed insurance loss data ⋮ Modelling insurance losses using a new beta power transformed family of distributions ⋮ On Parametrization of Multivariate Skew-Normal Distribution ⋮ Estimating the Probability of a Rare Event via Elliptical Copulas ⋮ Weighted Pricing Functionals With Applications to Insurance

Uses Software

• sn

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Wang's capital allocation formula for elliptically contoured distributions.
• Skewed multivariate models related to hidden truncation and/or selective reporting. With discussion and a rejoinder by the authors.
• Coherent Measures of Risk
• The multivariate skew-normal distribution
• The Skew-normal Distribution and Related Multivariate Families*
• Tail Conditional Expectations for Exponential Dispersion Models
• Economic Capital Allocation Derived from Risk Measures
• Tail Conditional Expectations for Elliptical Distributions
• A general class of multivariate skew-elliptical distributions

This page was built for publication: Multivariate skew-normal distributions with applications in insurance