Copula Theory and Its Applications: Proceedings of the by Piotr Jaworski

By Piotr Jaworski

Copulas are mathematical items that absolutely catch the dependence constitution between random variables and as a result supply nice flexibility in development multivariate stochastic versions. seeing that their creation within the early 50's, copulas have received substantial reputation in numerous fields of utilized arithmetic, equivalent to finance, assurance and reliability conception. this present day, they symbolize a well-known device for marketplace and credits versions, aggregation of dangers, portfolio choice, and so forth. This publication is split into major components: half I - "Surveys" comprises eleven chapters that offer an updated account of crucial points of copula versions. half II - "Contributions" collects the prolonged types of 6 talks chosen from papers awarded on the workshop in Warsaw.

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Extra info for Copula Theory and Its Applications: Proceedings of the Workshop Held in Warsaw, 25-26 September 2009

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Fd (xd )) . 11) Such a C is uniquely determined on A1 × A2 × · · · × Ad and, hence, it is unique when F1 , F2 ,. . , Fd are all continuous. Sklar’s theorem has been announced in [192], however its first proof for the bivariate case appeared in [185]. Curiously, it should be noted that in [192], the author “Abe Sklar” is named as “M. ” should be intended as “Monsieur”). Another (bivariate) proof can be also found in [16], based on the so-called “checkerboard copulas”. 2]). Another possible proof can be also derived (for positive random variables) from [14].

Multivar. Anal. 99(10), 2234–2250 (2008) 126. : Discussion of: “Copulas: tales and facts” by T. Mikosch [Extremes 9 (2006), no. 1, 3–20]. Extremes 9(1), 43–44 (2006) 1 Copula Theory: An Introduction 29 127. : Efficiently sampling exchangeable Cuadras-Augé copulas in high dimensions. Inform. Sci. 179(17), 2872–2877 (2009) 128. : Lévy-Frailty copulas. J. Multivar. Anal. 100(7), 1567–1585 (2009) 129. : Reparameterizing Marshall-Olkin copulas with applications to highdimensional sampling. J. Stat. Comput.

For such problems, a dramatic underestimation of the risk can be obtained when one tries to fit with copulas that do not exhibit any peculiar behaviour in the tails. This was exactly one of the main criticisms to the use of Li’s model for credit risk using Gaussian copulas (see, for example, [121, 198]). Inspired by some considerations of Joe [104], we discuss here some general properties that a “good” family of multivariate copulas {Cθ }, where θ is a parameter belonging to a (usually, compact) subset Θ ⊆ R p (p ≥ 1), should have for being considered “interesting” in statistical applications.

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