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

By Piotr Jaworski

ISBN-10: 364212464X

ISBN-13: 9783642124648

Copulas are mathematical gadgets that totally seize the dependence constitution between random variables and therefore provide nice flexibility in construction multivariate stochastic types. on account that their creation within the early 50's, copulas have received substantial acceptance in numerous fields of utilized arithmetic, comparable to finance, assurance and reliability concept. this present day, they signify a well-known software for industry and credits versions, aggregation of dangers, portfolio choice, and so on. This booklet is split into major components: half I - "Surveys" comprises eleven chapters that offer an updated account of crucial features of copula versions. half II - "Contributions" collects the prolonged types of 6 talks chosen from papers provided on the workshop in Warsaw.

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

Example text

Concepts, techniques and tools. Princeton Series in Finance. Princeton University Press, Princeton, NJ (2005) 139. : Ordinal sums and idempotents of copulas. Aequationes Math. 79 (1–2), 39–52 (2010) 140. : Copulas: tales and facts. Extremes 9(1), 3–20 (2006) 141. : “Copulas: tales and facts” [Extremes 9 (2006), no. 1, 3–20]—rejoinder. Extremes 9(1), 55–62 (2006) 142. : Some approximations of n-copulas. Metrika (2009). In press 143. : Probabilistic interpretations of copulas and their convex sums.

Xd ) = C F 1 (x1 ), F 2 (x2 ), . . , F d (xd ) . 13) for some copula C, usually called survival copula of X (to be intended as a copula associated with the survival function of X). 14 Fabrizio Durante and Carlo Sempi In particular, let C be the copula of X and let U = (U1 ,U2 , . . ,Ud ) be a vector such that U ∼ C. Then, one has C(u) = C(1 − u1 , 1 − u2 , . . , 1 − ud ), where C(u) = P(U1 > u1 ,U2 > u2 , . . ,Ud > ud ) is the survival function associated with C, explicitly given by d C(u) = 1 + ∑ (−1)k k=1 ∑ 1≤i1

Fg . This fact represents a limitation to the use of such distributions for modelling stochastic 1 Copula Theory: An Introduction 17 systems when the components are not similar. ’s, for obtaining more flexible models. 2, are usually called meta-elliptical distribution [63]. 1. Let X be an elliptical random vector, X ∼ Ed (μ , Σ , g). Suppose √ that, for every i ∈ {1, 2, . . , d}, (Xi / σii ) ∼ Fg . We call elliptical copula the distribution function of the random vector X1 √ σ11 Fg , Fg X2 √ σ22 Xd √ σdd , .

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Copula Theory and Its Applications: Proceedings of the Workshop Held in Warsaw, 25-26 September 2009 by Piotr Jaworski


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