
@article{cherubini2009,
  title = {Computing the {{Volume}} of {\emph{n}} -{{Dimensional Copulas}}},
  author = {Cherubini, Umberto and Romagnoli, Silvia},
  year = {2009},
  month = oct,
  volume = {16},
  pages = {307--314},
  issn = {1350-486X, 1466-4313},
  abstract = {A problem that is very relevant in applications of copula functions to finance is the computation of the survival copula, which is applied to enforce multivariate put\textendash{}call parity. This may be very complex for large dimensions. The problem is a special case of the more general problem of volume computation in high-dimensional copulas. We provide an algorithm for the exact computation of the volume of copula functions in cases where the copula function is computable in closed form. We apply the algorithm to the problem of computing the survival of a copula function in the pricing problem of a multivariate digital option, and we provide evidence that this is feasible for baskets of up to 20 underlying assets, with acceptable CPU time performance.},
  journal = {Applied Mathematical Finance},
  keywords = {copula},
  language = {en},
  number = {4}
}

@article{cuberos2019,
  title = {Copulas Checker-Type Approximations: {{Application}} to Quantiles Estimation of Sums of Dependent Random Variables},
  shorttitle = {Copulas Checker-Type Approximations},
  author = {Cuberos, A. and Masiello, E. and {Maume-Deschamps}, V.},
  year = {2019},
  month = mar,
  pages = {1--19},
  issn = {0361-0926, 1532-415X},
  abstract = {Several approximations of copulas have been proposed in the literature. By using empirical versions of checker-type copulas approximations, we propose non parametric estimators of the copula. Under some conditions, the proposed estimators are copulas and their main advantage is that they can be sampled from easily. One possible application is the estimation of quantiles of sums of dependent random variables from a small sample of the multivariate law and a full knowledge of the marginal laws. We show that estimations may be improved by including in an easy way in the approximated copula some additional information on the law of a sub-vector for example. Our approach is illustrated by numerical examples.},
  journal = {Communications in Statistics - Theory and Methods},
  keywords = {copula},
  language = {en}
}

@article{durante2013,
  title = {Multivariate Patchwork Copulas: {{A}} Unified Approach with Applications to Partial Comonotonicity},
  shorttitle = {Multivariate Patchwork Copulas},
  author = {Durante, Fabrizio and Fern{\'a}ndez S{\'a}nchez, Juan and Sempi, Carlo},
  year = {2013},
  month = nov,
  volume = {53},
  pages = {897--905},
  issn = {01676687},
  abstract = {We present a general view of patchwork constructions of copulas that encompasses previous approaches based on similar ideas (ordinal sums, gluing methods, piecing-together, etc.). Practical applications of the new methodology are connected with the determination of copulas having specified behaviour in the tails, such as upper comonotonic copulas.},
  journal = {Insurance: Mathematics and Economics},
  keywords = {copula},
  language = {en},
  number = {3}
}

@article{durante2015,
  title = {Convergence Results for Patchwork Copulas},
  author = {Durante, Fabrizio and {Fern{\'a}ndez-S{\'a}nchez}, Juan and {Quesada-Molina}, Jos{\'e} Juan and {\'U}beda-Flores, Manuel},
  year = {2015},
  month = dec,
  volume = {247},
  pages = {525--531},
  issn = {03772217},
  abstract = {We present a general construction that allows to extend a given subcopula to a copula in such a way that the extension is affine on some specific segments of the copula domain. This construction is hence applied to provide convergence theorems for approximating a copula in strong convergence and in D1-metric (related to the Markov kernel representation of a copula).},
  journal = {European Journal of Operational Research},
  keywords = {copula},
  language = {en},
  number = {2}
}

@article{genest2017,
  title = {Asymptotic Behavior of the Empirical Multilinear Copula Process under Broad Conditions},
  author = {Genest, Christian and Ne{\v s}lehov{\'a}, Johanna G. and R{\'e}millard, Bruno},
  year = {2017},
  month = jul,
  volume = {159},
  pages = {82--110},
  issn = {0047259X},
  abstract = {The empirical checkerboard copula is a multilinear extension of the empirical copula, which plays a key role for inference in copula models. Weak convergence of the corresponding empirical process based on a random sample from the underlying multivariate distribution is established here under broad conditions which allow for arbitrary univariate margins. It is only required that the underlying checkerboard copula has continuous first-order partial derivatives on an open subset of the unit hypercube. This assumption is very weak and always satisfied when the margins are discrete. When the margins are continuous, one recovers the limit of the classical empirical copula process under conditions which are comparable to the weakest ones currently available in the literature. A multiplier bootstrap method is also proposed to replicate the limiting process and its validity is established. The empirical checkerboard copula is further shown to be a more precise estimator of the checkerboard copula than the empirical copula based on jittered data. Finally, the weak convergence of the empirical checkerboard copula process is shown to be sufficiently strong to derive the asymptotic behavior of a broad class of functionals that are directly relevant for the development of rigorous statistical methodology for copula models with arbitrary margins.},
  journal = {Journal of Multivariate Analysis},
  keywords = {copula},
  language = {en}
}

@article{laverny2020,
  title = {Dependence Structure Estimation Using Copula Recursive Trees},
  author = {Laverny, Oskar and {Maume-Deschamps}, V{\'e}ronique and Masiello, Esterina and Rulli{\`e}re, Didier},
  year = {2020},
  archivePrefix = {arXiv},
  copyright = {All rights reserved},
  journal = {arXiv preprint arXiv:2005.02912},
  keywords = {Mathematics - Statistics Theory}
}
