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A FORM OF MULTIVARIATE PARETO DISTRIBUTION WITH APPLICATIONS TO FINANCIAL RISK MEASUREMENT

Published online by Cambridge University Press:  31 August 2016

Jianxi Su  and
Edward Furman
Jianxi Su
Affiliation:
Department of Mathematics and Statistics, York University, Toronto, Ontario M3J 1P3, Canada
Edward Furman*
Affiliation:
Department of Mathematics and Statistics, York University, Toronto, Ontario M3J 1P3, Canada
*
E-Mail: [email protected]
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Abstract

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A new multivariate distribution possessing arbitrarily parametrized and positively dependent univariate Pareto margins is introduced. Unlike the probability law of Asimit et al. (2010), the structure in this paper is absolutely continuous with respect to the corresponding Lebesgue measure. The distribution is of importance to actuaries through its connections to the popular frailty models, as well as because of the capacity to describe dependent heavy-tailed risks. The genesis of the new distribution is linked to a number of existing probability models, and useful characteristic results are proved. Expressions for, e.g., the decumulative distribution and probability density functions, (joint) moments and regressions are developed. The distributions of minima and maxima, as well as, some weighted risk measures are employed to exemplify possible applications of the distribution in insurance.

Keywords

Multivariate Pareto distributionscharacterizationsdependenceweighted risk measuresminimamaxima
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 47 , Issue 1 , January 2017 , pp. 331 - 357
Copyright
Copyright © Astin Bulletin 2016 

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