Modelowanie struktur zależności za pomocą funkcji połączeń w analizie ryzyka ubezpieczyciela

Abstract

This paper aims to present copulas, as a modeling tool which will give the 'richer' dependency structures than the use of linear correlation. The paper presents definitions and basic properties of the copula function. Discusses its relationship with the basic types of dependencies used in risk management i.e. comonotonicity, countermonotonicity, independence and linear dependence and the basic measures of dependence (Pearson's correlation, Kendall's rank correlation, Spearman's rank correlation, Blomqvist's beta, upper (lower) tail dependence parameter). Then selected family of copulas have been characterized and is an example of construction of two-dimensional dis- tribution, where the marginal distributions are known and the Kendall's rank correlation between them. Calculations and graphs were performed using the package „R”.