Tail Conditional Expectation for Multivariate Pareto Portfolio

Determination of risk capital is a subject of active interest to researchers, regulators of financial institutes 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. TCE represents the conditional average amount of loss that can be incurred in a particular period, given that the loss exceeds a specified value. This value is usually based on a quantile of the distribution, the so-called value-at-risk (VaR). The present study examines the TCE in the case of multivariate Pareto distribution. We show that the divided differences, actually important in the numerical analysis and polynomial's approximations, are quite convenient tool on the capital asset allocation problem in the multivariate dependent Pareto context.