On a Multivariate Pareto Distribution

Abstract

A multivariate distribution possessing arbitrarily parameterized Pareto margins is formulated and studied. The distribution is believed to allow for an adequate modeling of dependent heavy tailed risks with a non-zero probability of simultaneous loss. Numerous links to certain nowadays existing probabilistic models, as well as seemingly useful characteristic results are proved. Expressions for, e.g., decumulative distribution functions, densities, (joint) moments and regressions are developed. An application to the classical pricing problem is considered, and some formulas are derived using the recently introduced economic weighted premium calculation principles.

Keywords: Multivariate Pareto distributions, Characterizations, Mixtures, Dependence, Simultaneous Loss, Economic Weighted Pricing

JEL Classification: C10, C60