COPULAS AND EVALUATION OF TVaR RISK MEASUREMENT AND TVaR-BASED CAPITAL ALLOCATION IN A CONTEXT OF TAIL DEPENDENCY

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Résumé

In this paper, we construct an extension of Spearman’s copula and
evaluate the risk measure TVaR (Tail Value at Risk) and the TVaRbased capital allocation for an insurance portfolio whose risks
maintain a tail-dependency relationship via this new copula. Assuming
that the portfolio comprises two lines of business whose risks are
identically distributed according to the exponential law and then
according to the Pareto law, we derive an explicit formula for the risk
measure TVaR and the explicit formula for the capital to be allocated
to each line of business in the portfolio to ensure the solvency of the
insurance company.

Mots-clés

copula, tail dependency, TVaR risk measure, capital allocation.