By Piotr Jaworski

Copulas are mathematical gadgets that totally trap the dependence constitution between random variables and accordingly supply nice flexibility in development multivariate stochastic types. when you consider that their creation within the early 50's, copulas have won enormous attractiveness in numerous fields of utilized arithmetic, equivalent to finance, assurance and reliability conception. this present day, they characterize a well-known device for industry and credits types, aggregation of hazards, portfolio choice, and so forth. This booklet is split into major elements: half I - "Surveys" includes eleven chapters that offer an updated account of crucial elements 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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Stat. Probab. Lett. 66(3), 315–325 (2004) 171. : Multivariate copulas with quadratic sections in one variable. Metrika (2009). In press 172. : Some new characterizations and properties of quasi-copulas. Fuzzy Sets Syst. 160(6), 717–725 (2009) 173. : Sharpness of Fréchet-bounds. Z. Wahrsch. Verw. Gebiete 57(2), 293–302 (1981) 174. : Construction of multivariate distributions with given marginals. Ann. Inst. Stat. Math. 37(2), 225–233 (1985) 175. : On the distributional transform, Sklar’s Theorem, and the empirical copula process.

Here, we present the EFGM family of copulas that can be derived from the papers just mentioned. Let d ≥ 2. Let S be the class of all subsets of {1, 2, . . , d} having at least 2 elements. Trivially, S contains 2d − d − 1 elements. To each S ∈ S , we associate a real number αS , with the convention that, when S = {i1 , i2 , . . ik . 21) j∈S for suitable values of the αS ’s. 22) and C3EFGM (u1 , u2 , u3 ) = u1 u2 u3 [1 + α12 (1 − u1 )(1 − u2 ) + α13 (1 − u1 )(1 − u3 ) + α23 (1 − u2 )(1 − u3 ) + α123 (1 − u1 )(1 − u2 )(1 − u3 )].

1, 3–20]. Extremes 9(1), 45–47 (2006) 57. : Copulas: a personal view. J. Risk Ins. 76(3), 639–650 (2009) 58. : Correlation and dependence in risk management: properties and pitfalls. In: Dempster, M. ) Risk Management: Value at Risk and Beyond, pp. 176–223. Cambridge University Press, Cambridge (2002) 59. : Risk aggregation. , Rychlik, T. ) Copula Theory and Its Applications, Proceedings of the Workshop, Warsaw, 25–26 Sept 2009. Springer, Dordrecht (2010) 60. : On the construction of families of absolutely continuous copulas with given restrictions.

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