Modeling Dependence Using Skew T Copulas: Bayesian Inference and Applications

Multivariate dependence modeling using copulas

In this contribution we review models for construction of higher dimensional dependence that have arisen recent years. In particular we focus on specific generalized Farlie Gumbel (or Sarmanov) copulas which are generated by a single function (so-called generator or generator function) defined on the unit interval. An alternative approach to generalize the FGM family of copulas is to consider t...

Modeling dependence between loss triangles using copulas

A critical problem in property and casualty insurance is forecasting payments for incurred but not yet finalized claims. Forecasts and associated risk margins are often based on loss triangles with each triangle corresponding to a different line of business. Each triangle displays the development over time of all payments associated with claims originating in each year and for a given line of b...

Modeling tail dependence using copulas — literature review

Modeling dependence between random variables using copulas

The concept of copulas is normaly used to model the dependence structure between two or more random variables. Random variables are transformed to the unit interval I = [0, 1] by using quasi-inverse transformation. As a result we get a normalised multivariate distribution function called the copula. Copulas uniquely determine the dependence structure of multiple random variables. The aim of the...

Bayesian inference for multivariate copulas using pair-copula constructions

This article provides a Bayesian analysis of pair-copula constructions (Aas et al., 2007 Insurance Math. Econom.) for modeling multivariate dependence structures. These constructions are based on bivariate t−copulas as building blocks and can model the nature of extremal events in bivariate margins individually. According to recent empirical studies (Fischer et al. (2007) and Berg and Aas (2007...