On a Family of Log-Gamma-Generated Archimedean Copulas

Abstract

Modeling dependence structure among various risks, especially the measure of tail dependence and the aggregation of risks, is crucial for risk management. In this article, we present an extension to the traditional one-parameter Archimedean copulas by integrating the log-gamma-generated (LGG) margins. This class of novel multivariate distribution can better capture the tail dependence. The distortion effect on the classic one-parameter Archimedean copulas is well exhibited and the analytical expression of the sum of bivariate margins is proposed. The model provides a flexible way to capture tail risks and aggregate portfolio losses. Sufficient conditions for constructing a legitimate d-dimensional LGG Archimedean copula as well as the simulation framework are also proposed. Furthermore, two applications of this model are presented using concrete insurance datasets.