Assessing High-Risk Scenarios by Full-Range Tail Dependence Copulas

The Casualty Actuarial Society, Canadian Institute of Actuaries, and the Society of Actuaries' Joint Risk Management Section is pleased to make available a research report exploring how a full-range tail dependence copula would be useful in assessing tail risks in a regression setting. The report was authored by Lei Hua and Michelle Xia. Copulas with a full-range tail dependence property can cover the widest range of positive dependence in the tail, so that a regression model can be built accounting for dynamic tail dependence patterns between variables. We propose a model that incorpo-rates both regression on each marginal of bivariate response variables and regression on the dependence parameter for the response variables. ACIG copula that possesses the full-range tail dependence property is implemented in the regression analysis. Comparisons between regression analysis based on ACIG and Gumbel copulas are conducted, showing that ACIG is generally better than Gumbel copula when there is intermediate upper tail dependence. A simulation study is conducted to illustrate that dynamic tail dependence structures between loss and ALAE can be captured by using the one-parameter ACIG copula. Finally, we apply the ACIG and Gumbel regression models respectively for a dataset from the Medical Expenditure Panel Survey of the United States.