• Corpus ID: 248986734

Exchangeable FGM copulas

  title={Exchangeable FGM copulas},
  author={Christopher Blier-Wong and H{\'e}l{\`e}ne Cossette and {\'E}tienne Marceau},
Copulas are a powerful tool to model dependence between the components of a random vector. One well-known class of copulas when working in two dimensions is the Farlie-Gumbel-Morgenstern (FGM) copula since their simple analytic shape enables closed-form solutions to many problems in applied probability. However, the classical definition of high-dimensional FGM copula does not enable a straightforward understanding of the effect of the copula parameters on the dependence, nor a geometric… 
3 Citations

Figures and Tables from this paper

Risk aggregation with FGM copulas

This paper builds on two novel representations of FGM copulas based on symmetric multivariate Bernoulli distributions and order statistics, providing a new perspective on risk aggregation with FGMCopulas and risk-sharing and capital allocation.

A new method to construct high-dimensional copulas with Bernoulli and Coxian-2 distributions

We propose an approach to construct a new family of generalized Farlie-Gumbel-Morgenstern (GFGM) copulas that naturally scales to high dimensions. A GFGM copula can model moderate positive and

Collective risk models with FGM dependence

We study copula-based collective risk models when the dependence structure is defined by a Farlie-Gumbel-Morgenstern copula. By leveraging a one-to-one correspondence between the class of



The empirical beta copula

Principles of Copula Theory

Copulas: Basic Definitions and Properties Notations Preliminaries on random variables and distribution functions Definition and first examples Characterization in terms of properties of d.f.s

Statistical Inference Procedures for Bivariate Archimedean Copulas

Abstract A bivariate distribution function H(x, y) with marginals F(x) and G(y) is said to be generated by an Archimedean copula if it can be expressed in the form H(x, y) = ϕ–1[ϕ{F(x)} + ϕ{G(y)}]

Financial engineering with copulas explained

The book will show, from a financial engineering perspective, how copula theory can be applied in the context of portfolio credit-risk modeling, and how it can help to derive model-free bounds for relevant risk measures.

Effective estimation algorithm for parameters of multivariate Farlie–Gumbel–Morgenstern copula

This paper focuses on the parameter estimation for the d-variate Farlie–Gumbel–Morgenstern (FGM) copula ($$d\ge 2$$ d ≥ 2 ), which has $$2^d-d-1$$ 2 d - d - 1 dependence

An Introduction to Copulas

These notes provide an introduction to modeling with copulas. Copulas are the mechanism which allows us to isolate the dependency structure in a multivariate distribution. In particular, we can

On the Moments of Aggregate Discounted Claims with Dependence Introduced by a FGM Copula

Abstract In this paper, we investigate the computation of the moments of the compound Poisson sums with discounted claims when introducing dependence between the interclaim time and the subsequent


We define the Bernstein copula and study its statistical properties in terms of both distributions and densities. We also develop a theory of approximation for multivariate distributions in terms of

Detection of block-exchangeable structure in large-scale correlation matrices

A copula method for modeling directional dependence of genes

This method is able to overcome the limitation of Bayesian network method for gene-gene interaction, i.e. information loss due to binary transformation, and can be an alternative to Bayesian networks in modeling gene interactions.