Based on the trivariate pair-copula construction for the bivariate linear circular copula by Perlman and Wellner (Symmetry 3:574-99, 2011) and the Theorem of Carathéodory, which states that any valid correlation matrix is a finite convex combination of extreme correlation matrices, we generate a class of closed-form analytical 3-universal copulas. We derive explicit product and lifting copula f...

Abstract. We consider copulas with a given diagonal section and compute the explicit density of the unique optimal copula which maximizes the entropy. In this sense, this copula is the least informative among the copulas with a given diagonal section. We give an explicit criterion on the diagonal section for the existence of the optimal copula and give a closed formula for its entropy. We also ...

This chapter introduces copula functions and the use of the Gaussian copula function to model probabilistic dependencies in supervised classification tasks. A copula is a distribution function with the implicit capacity to model non linear dependencies via concordance measures, such as Kendall’s τ . Hence, this chapter studies the performance of a simple probabilistic classifier based on the Ga...

Abstract The Pearson product-moment correlation commonly used as statistical dependence measure was developed assuming normal marginal and addresses only linear dependence. In most applications, the distribution is assumed to be a multivariate normal or lognormal for tractable calculus even if the assumption may not be appropriate. A copula based approach couples marginal distributions to form ...

Conditional copula models are flexible tools for modelling complex dependence structures in regression settings. We construct Bayesian inference for the conditional copula model adapted to regression settings in which the bivariate outcome is continuous or mixed. The dependence between the copula parameter and the covariate is modelled using cubic splines. The proposed joint Bayesian inference ...

The tail copula is widely used to describe the dependence in the tail of multivariate distributions. In some situations such as risk management, the dependence structure may be linked with some covariate. The tail copula thus depends on this covariate and is referred to as the conditional tail copula. The aim of this paper is to propose a nonparametric estimator of the conditional tail copula a...

Given a copula C, we examine under which conditions on an order isomorphism ψ of [0, 1], the distortion Cψ : [0, 1] → [0, 1], Cψ(x, y) = ψ(C(ψ−1(x)), ψ−1(y)), is again a copula. In particular, when the copula C is totally positive of order 2, we give a sufficient condition on ψ which ensures that any distortion of C by means of ψ is again a copula. The presented results allow us to introduce in...

Motivated by the wide applications of distortion function and copulas in insurance and finance, this paper generalizes the notion of deterministic distortion function to a stochastic distortion function, i.e., a random process, and employs the defined stochastic distortion function to construct a so-called stochastic distorted copula. One method for constructing stochastic distortions is provid...

Modeling short and long time dependence in univariate time series may be successfully accomplished through existing time series processes. In the multivariate setting just a few complex models exist to take care of the di®erent marginal dynamics as well as of the dynamic covariance matrix. The copula approach factors the joint distribution into the marginals and a dependence function, its copul...

Abstract T his paper empirically examines the impact of dependence structure between the assets on the portfolio optimization, composed of Tehran Stock Exchange Price Index and Borsa Istanbul 100 Index. In this regard, the method of the Copula family functions is proposed as powerful and flexible tool to determine the structure of dependence. Finally, the impact of the dep...