Geodesic
Construction of multivariate copulas in $n$-boxes
Kybernetika, Tome 49 (2013) no. 1, pp. 73-95 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper we give an alternative proof of the construction of $n$-dimensional ordinal sums given in Mesiar and Sempi [17], we also provide a new methodology to construct $n$-copulas extending the patchwork methodology of Durante, Saminger-Platz and Sarkoci in [6] and [7]. Finally, we use the gluing method of Siburg and Stoimenov [20] and its generalization in Mesiar et al. [15] to give an alternative method of patchwork construction of $n$-copulas, which can be also used in composition with our patchwork method.
In this paper we give an alternative proof of the construction of $n$-dimensional ordinal sums given in Mesiar and Sempi [17], we also provide a new methodology to construct $n$-copulas extending the patchwork methodology of Durante, Saminger-Platz and Sarkoci in [6] and [7]. Finally, we use the gluing method of Siburg and Stoimenov [20] and its generalization in Mesiar et al. [15] to give an alternative method of patchwork construction of $n$-copulas, which can be also used in composition with our patchwork method.
Classification : 60A10, 60E05
Keywords: $n$-copulas; modular functions; rectangular patchwork 
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González-Barrios, José M.; Hernández-Cedillo, María M. Construction of multivariate copulas in $n$-boxes. Kybernetika, Tome 49 (2013) no. 1, pp. 73-95. http://geodesic.mathdoc.fr/item/KYB_2013_49_1_a5/

[1] Aczél, J., Dhombres, J.: Functional Equations in Several Variables. Cambridge University Press, Cambridge 1989. | MR | Zbl

[2] Baets, B. De, Meyer, H. De: Orthogonal grid constructions of copulas. IEEE Trans. Fuzzy Systems 15 (2007), 6, 1053-1062. | DOI

[3] Cherubini, U., Luciano, E., Vecchiato, W.: Copula Methods in Finance. John Wiley and Sons, Chichester 2004. | MR | Zbl

[4] Dorey, M., Joubert, P.: Modelling copulas: An overview. The Staple Inn Actuarial Society, London 2005.

[5] Durante, F., Kolesárová, A., Mesiar, R., Sempi, C.: Copulas with given diagonal sections: novel constructions and applications. Internat. J. Uncertain. Fuzziness Knowledge-Based Systems 15 (2007), 397-410. | DOI | MR | Zbl

[6] Durante, F., Saminger-Platz, S., Sarkoci, P.: On representations of 2-increasing binary aggregation functions. Inform. Sci. 178 (2008), 4534-4541. | DOI | MR | Zbl

[7] Durante, F., Saminger-Platz, S., Sarkoci, P.: Rectangular patchwork for bivariate copulas and tail dependence. Comm. Statist. Theory Methods 38 (2009), 2515-2527. | DOI | MR | Zbl

[8] Durante, F., Fernández-Sánchez, J.: Multivariate shuffles and approximation of copulas. Statist. Probab. Lett. 80 (2010), 1827-1834. | DOI | MR | Zbl

[9] Embrechts, P., Höing, A., Juri, A.: Using copulae to bound the value-at-risk for functions of dependent risks. Finance Stochast. 7 (2003), 145-167. | DOI | MR | Zbl

[10] Erdely, A., Díaz-Vieira, M.: Nonparametric and semiparametric bivariate modeling of petrophysical porosity-permeability dependence from well log data. In: Copula Theory and Its Applications (P. Jaworski, F. Durante, W. K. Härdle and T. Rychlik, eds.), Lect. Notes in Statistics, Springer (2010), pp. 267-278.

[11] Hernández-Cedillo, M. M.: Topics on multivariate copulas and applications. Ph. D. Thesis, Universidad Nacional Autónoma de México 2013.

[12] Joe, H.: Multivariate Models and Dependence Concepts. Chapman and Hall, London 1997. | MR | Zbl

[13] Klement, E. P., Kolesárová, A., Mesiar, R., Sempi, C.: Copulas constructed from the horizontal section. Comm. Statist. Theory Methods 36 (2007), 2901-2911. | DOI | MR

[14] Malevergne, Y., Sornette, D.: Extreme Financial Risk. From Dependence to Risk Management. Springer-Verlag, Berlin 2006. | MR

[15] Mesiar, R., Jágr, V., Juráňová, M., Komorníková, M.: Univariate conditioning of copulas. Kybernetika 44 (2008), 6, 807-816. | MR | Zbl

[16] McNeil, A. J., Frey, R., Embrechts, P.: Quantitative Risk Management. Princeton University Press, Princeton 2005. | MR | Zbl

[17] Mesiar, R., Sempi, C.: Ordinal sums and idempotent of copulas. Aequationes Math. 79 (2010), 1-2, 39-52. | DOI | MR

[18] Nelsen, R. B.: An Introduction to Copulas. Second edition. Springer, New York 2006. | MR | Zbl

[19] Salvadori, G., Michele, C. De, Kottegoda, N. T., Rosso, R.: Extremes in Nature. An Approach Using Copulas. Series: Water Science and Technology Library 56, Springer, Amsterdam 2007.

[20] Siburg, K. F., Stoimenov, P. A.: Gluing copulas. Comm. Statist. Theory Methods 37 (2008), 3124-3134. | DOI | MR

[21] Zhang, M. H.: Modelling total tail dependence along diagonals. Insur. Math. Econ. 42 (2008), 73-80. | DOI | MR | Zbl