  Analysing dependent risks is an important task for insurance companies. A
dependency is reflected in the fact that information about one random variable
provides information about the likely distribution of values of another random
variable. Insurance companies in particular must investigate such dependencies
between different lines of business and the effects that an extreme loss event,
such as an earthquake or hurricane, has across multiple lines of business
simultaneously. Copulas provide a popular model-based approach to analysing the
dependency between risks, and the coefficient of tail dependence is a measure
of dependence for extreme losses. Besides commonly used empirical estimators
for estimating the tail dependence coefficient, copula fitting can lead to
estimation of such coefficients directly or can verify their existence.
Generally, a range of copula models is available to fit a data set well,
leading to multiple different tail dependence results; a method based on
Bayesian model averaging is designed to obtain a unified estimate of tail
dependence. In this article, this model-based coefficient estimation method is
illustrated through a variety of copula fitting approaches and results are
presented for several simulated data sets and also a real general insurance
loss data set.
