Related papers: Risk aggregation with FGM copulas
The study of sums of possibly associated Bernoulli random variables has been hampered by an asymmetry between positive correlation and negative correlation. The Conway-Maxwell Binomial (COMB) distribution and its multivariate extension, the…
We propose a novel distributional regression model for a multivariate response vector based on a copula process over the covariate space. It uses the implicit copula of a Gaussian multivariate regression, which we call a ``regression…
Using a family of modified Weibull distributions, encompassing both sub-exponentials and super-exponentials, to parameterize the marginal distributions of asset returns and their natural multivariate generalizations, we give exact formulas…
Understanding variable dependence, particularly eliciting their statistical properties given a set of covariates, provides the mathematical foundation in practical operations management such as risk analysis and decision-making given…
Several collective risk models have recently been proposed by relaxing the widely used but controversial assumption of independence between claim frequency and severity. Approaches include the bivariate copula model, random effect model,…
In this paper we propose a Farlie-Gumbel-Morgenstern (FGM) family of bivariate linear exponential distributions generated from given marginal's. Therefore, properties of FGM are analogous to properties of bivariate distributions. We study…
Thanks to their ability to capture complex dependence structures, copulas are frequently used to glue random variables into a joint model with arbitrary marginal distributions. More recently, they have been applied to solve statistical…
We propose a semiparametric family of copulas based on a set of orthonormal functions and a matrix. This new copula permits to reach values of Spearman's Rho arbitrarily close to one without introducing a singular component. Moreover, it…
In order to properly manage risk, practitioners must understand the aggregate risks they are exposed to. Additionally, to properly price policies and calculate bonuses the relative riskiness of individual business units must be well…
Aggregation sets, which represent model uncertainty due to unknown dependence, are an important object in the study of robust risk aggregation. In this paper, we investigate ordering relations between two aggregation sets for which the sets…
In this paper, we consider the multivariate Bernoulli distribution as a model to estimate the structure of graphs with binary nodes. This distribution is discussed in the framework of the exponential family, and its statistical properties…
In this paper we obtain closed expressions for the probability distribution function, when we consider aggregated risks with multivariate dependent Pareto distributions. We work with the dependent multivariate Pareto type II proposed by…
We present a constructive and self-contained approach to data driven infinite partition-of-unity copulas that were recently introduced in the literature. In particular, we consider negative binomial and Poisson copulas and present a…
We construct new multivariate copulas on the basis of a generalized infinite partition-of-unity approach. This approach allows - in contrast to finite partition-of-unity copulas - for tail-dependence as well as for asymmetry. A possibility…
Distributional regression aims at estimating the conditional distribution of a targetvariable given explanatory co-variates. It is a crucial tool for forecasting whena precise uncertainty quantification is required. A popular methodology…
This paper investigates Gaussian copula mixture models (GCMM), which are an extension of Gaussian mixture models (GMM) that incorporate copula concepts. The paper presents the mathematical definition of GCMM and explores the properties of…
We show an analytic method to construct a bivariate distribution function (DF) with given marginal distributions and correlation coefficient. We introduce a convenient mathematical tool, called a copula, to connect two DFs with any…
This paper presents comparison results and establishes risk bounds for credit portfolios within classes of Bernoulli mixture models, assuming conditionally independent defaults that are stochastically increasing with a common risk factor.…
The inf-convolution of risk measures is directly related to risk sharing and general equilibrium, and it has attracted considerable attention in mathematical finance and insurance problems. However, the theory is restricted to finite sets…
Copulas are a powerful tool for modeling multivariate distributions as they allow to separately estimate the univariate marginal distributions and the joint dependency structure. However, known parametric copulas offer limited flexibility…