2014 Centennial Celebration and Annual Meeting
Original Research Published in Variance: Reserving and Risk Management Models
Maximum likelihood estimators provide a powerful statistical tool. In this paper the authors directly deal with non-linear reserving models, without the need to transform those models to make them tractable for linear or generalized linear methods. They also show how the same general approach can be easily adapted to provide estimates for a very wide range of reserving methods and models, making use of the same framework, and even much of the same computer code. They focus on the triangle of incremental average costs, and show how five common methods can be set in a stochastic framework.
Second Paper: Interval Estimation for Bivariate t Copulas via Kendall’s Tau
Copula models have been popular in risk management. Due to the properties of asymptotic dependence and easy simulation, the t copula has often been employed in practice. A computationally simple estimation procedure for the t copula is to first estimate the linear correlation via Kendall’s tau estimator and then to estimate the parameter of the number of degrees of freedom by maximizing the pseudo likelihood function. In this paper, the authors derive the asymptotic limit of this two-step estimator which results in a complicate asymptotic covariance matrix. Further, they propose jackknife empirical likelihood methods to construct confidence intervals/regions for the parameters and the tail dependence coefficient without estimating any additional quantities. A simulation study shows that the proposed methods perform well in finite sample.