TVaR-Based Capital Allocation under Liouville Copulas

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DOI: https://doi.org/10.28924/2291-8639-23-2025-332
Published: Dec 12, 2025
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Fouad Marri, Khalil Said, TVaR-Based Capital Allocation under Liouville Copulas, Int. J. Anal. Appl., 23 (2025), 332.

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Fouad Marri, Khalil Said

Abstract

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.

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