Impact of dependence on some multivariate risk indicators

TL;DR

This paper investigates how dependence structures affect multivariate risk indicators and capital allocation, analyzing properties, asymptotic behavior, and the influence of copulas on allocation methods.

Contribution

It extends previous work by studying the properties and asymptotics of risk allocations under different dependence models, including copulas.

Findings

Allocation satisfies coherence axioms

Dependence structure significantly impacts allocation

Asymptotic behavior varies with distribution models

Abstract

The minimization of some multivariate risk indicators may be used as an allocation method, as proposed in C\'enac et al. [6]. The aim of capital allocation is to choose a point in a simplex, according to a given criterion. In a previous paper [17] we proved that the proposed allocation technique satisfies a set of coherence axioms. In the present one, we study the properties and asymptotic behavior of the allocation for some distribution models. We analyze also the impact of the dependence structure on the allocation using some copulas.