Assessing High - Risk Scenarios by Full - Range Tail Dependence Copulas Sponsored by CAS , CIA , SOA Joint Risk Management Section

The opinions expressed and conclusions reached by the authors are their own and do not represent any official position or opinion of the sponsoring organizations or their members. The sponsoring organizations make no representation or warranty to the accuracy of the information. Abstract. 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 incorporates 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. The empirical analysis suggests that the regression model with the ACIG copula improves the assessment of high-risk scenarios, especially for aggregated dependent risks. (CAS) and Canadian Institute of Actuaries (CIA). The financial support from SOA, CAS and CIA, and the precious time of the volunteers involved in proposal reviews and project oversights is greatly appreciated.