Copula Analysis of Insurance Tail Dependence in R

Speaker: Adrian O'Hagan (UCD)

The use of copulas to model extreme losses and capture tail dependence is becoming increasingly common among the actuarial community. A range of parametric copulas such as the t, Joe and Gumbel copula, among others, is available for this purpose. Each copula has an accompanying form of tail dependence coefficient, which can be readily estimated from the fitted copula and the loss data supplied.

However it is often unclear how to choose between competing copulas and their associated estimates of tail dependence when more than one copula provides reasonable fit to the data.

Bayesian Model Averaging (BMA) provides a convenient and statistically robust solution to this problem, allowing a weighted average of the tail dependence coefficients from different copulas to be combined to form a single, blended estimate of tail dependence.

The BMA process takes into account the size of the data set, the quality of copula fit (measured by its likelihood), and the complexity of each fitted copula (defined by its number of parameters). The method is illustrated and results presented for both simulated and real insurance loss data.