A form of multivariate Pareto distribution with applications to financial risk measurement

TL;DR

This paper introduces a new multivariate Pareto distribution with flexible dependence and continuous probability law, useful for modeling dependent heavy-tailed risks in finance and insurance.

Contribution

It presents a novel, absolutely continuous multivariate Pareto distribution with parametrized dependence, extending existing models and providing analytical expressions for key risk measures.

Findings

Distribution is absolutely continuous with respect to Lebesgue measure.

Derived expressions for distribution functions, moments, and regressions.

Demonstrated applications in insurance risk measurement.

Abstract

A new multivariate distribution possessing arbitrarily parametrized and positively dependent univariate Pareto margins is introduced. Unlike the probability law of Asimit et al. (2010) [Asimit, V., Furman, E. and Vernic, R. (2010) On a multivariate Pareto distribution. Insurance: Mathematics and Economics 46(2), 308-316], 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.