This article introduces actuaries to the concept of "copulas," a tool for understanding relationships among multivariate outcomes. A copula is a function that links univariate marginals to their full multivariate distribution. Copulas were introduced in 1959 in the context of probabilistic metric spaces. Recently, there has been a rapidly developing literature on the statistical properties and ...

Durante et al. (2007) introduced a class of bivariate copulas depending on two generators which generalizes some known families such as the Archimedean copulas. In this paper we provide some result on properties of this family when the generators are certain univariate survival functions.

This article introduces actuaries to the concept of ‘‘copulas,’’ a tool for understanding relationships among multivariate outcomes. A copula is a function that links univariate marginals to their full multivariate distribution. Copulas were introduced in 1959 in the context of probabilistic metric spaces. The literature on the statistical properties and applications of copulas has been develop...

We determine under which conditions three bivariate copulas C12, C13 and C23 are compatible, viz. they are the bivariate marginals of the same trivariate copula C̃, and, then, construct the class of these copulas. In particular, the upper and lower bounds for this class of trivariate copulas are determined.

= 0 if x j = 0 for at least one index j, and (3) all n-dimensional differences of C are nonnegative. There he further announced what we now call Sklar's theorem. In the Kybernetika paper he sketched the proof of the above statement, developed some of its consequences, and discussed various connections between copulas and random variables, associative copulas, binary operations on spaces of one-...

Multivariate exchangeable Archimedean copulas are one of the most popular classes of copulas that are used in actuarial science and finance for modelling risk dependencies and for using them to quantify the magnitude of tail dependence. Owing to the increase in popularity of copulas to measure dependent risks, generating multivariate copulas has become a very crucial exercise. Current methods f...

Although there exists a large variety of copula functions, only a few are practically manageable, and often the choice in dependence modeling falls on the Gaussian copula. Further, most copulas are exchangeable, thus implying symmetric dependence. We introduce a way to construct copulas based on periodic functions. We study the two-dimensional case based on one dependence parameter and then pro...

Program: 1. Fabrizio Durante (Free University of Bozen–Bolzano, Italy) Multivariate copulas with hairpin support 2. Piotr Jaworski (University of Warsaw, Poland) Copulas of self–similar Ito diffusions 3. Franco Pellerey (Politecnico di Torino, Italy) Univariate stochastic orders and joint stochastic orders: conditions on the copula for mutual relationships 4. Giovanni Puccetti (University of Fi...

This paper addresses the problem of efficiently sampling exchangeable and nested Archimedean copulas, with specific focus on large dimensions, where methods involving generator derivatives, such as the conditional distribution method, are not applicable. Additionally, new conditions under which Archimedean copulas can be mixed to construct nested Archimedean copulas are presented. Moreover, for...

Six different functions measuring the defect of a quasi-copula, i. e., how far away it is from a copula, are discussed. This is done by means of extremal non-positive volumes of specific rectangles (in a way that a zero defect characterizes copulas). Based on these defect functions, six transformations of quasi-copulas are investigated which give rise to six different partitions of the set of a...