TVaR-Based Capital Allocation under Liouville Copulas

Résumé

This paper provides explicit closed-form expressions for key tail risk measures, namely the Tail Value-at-Risk (TVaR) and TVaR-based capital allocation, in a multivariate risk framework governed by Liouville distributions. Introduced by McNeil and Nešlehová (2010), Liouville copulas offer a flexible and tractable class of models for capturing asymmetric and non-exchangeable dependencies. We derive analytical expressions for the distribution and survival functions of aggregate risks under various parametric specifications, including Clayton-Liouville and generalized Clayton-Liouville models. The conditions under which TVaR is finite are discussed in relation to the existence of moments. Numerical illustrations highlight the impact of dependence parameters and generator shapes on aggregate tail risk and its decomposition, demonstrating the practical relevance of Liouville-based models for capital modeling and solvency assessment.

Citer ce document

Accès au document

Texte intégral en lecture en ligne, réservé aux abonnés SPHAERO et aux membres de l'institution. Se connecter

Voir l'article sur le site de la revue

Auteur(s)

Statistiques

Consultations : 1

Téléchargements : 0