Multivariate Pareto portfolios: TCE-based capital allocation and divided differences

Abstract

Determination of risk capital is a subject of active interest to researchers, regulators of financial institutions, and commercial vendors of financial products and services. Recently, there has been growing concentration among the insurance companies and regulators on the use of tail conditional expectation (TCE) as measure of risk. The present study examines the TCE-based portfolio allocation for multivariate dependent Pareto risks. This family is broadly popular in actuarial sciences, mostly because of modeling heavy-tailed dependent losses. We show that the tool of divided differences, actually important in numerical analysis and polynomial's approximations, is quite convenient in the problem of capital asset allocation.