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- W3170202314 abstract "Based on the method of copulas, we construct a parametric family of multivariate distributions using mixtures of independent conditional distributions. The new family of multivariate copulas is a convex combination of products of independent and comonotone subcopulas. It fulfills the four most desirable properties that a multivariate statistical model should satisfy. In particular, the bivariate margins belong to a simple but flexible one-parameter family of bivariate copulas, called linear Spearman copula, which is similar but different to the convex family of Frechet. It is shown that the distribution and stop-loss transform of dependent sums from this multivariate family can be evaluated using explicit integral formulas, and that these dependent sums are bounded in convex order between the corresponding independent and comonotone sums. The model is applied to the evaluation of the economic risk capital for a portfolio of risks using conditional value-at-risk measures. A multivariate conditional value-at-risk vector measure is considered. Its components coincide for the constructed multivariate copula with the conditional value-at-risk measures of the risk components of the portfolio. This yields a “fair” risk allocation in the sense that each risk component becomes allocated its coherent conditional value-at-risk." @default.
- W3170202314 created "2021-06-22" @default.
- W3170202314 creator A5051104951 @default.
- W3170202314 date "2002-06-01" @default.
- W3170202314 modified "2023-09-23" @default.
- W3170202314 title "Multivariate Fréchet Copulas and Conditional Value-at-Risk" @default.
- W3170202314 hasPublicationYear "2002" @default.
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