摘要：Given an n x n triangle of losses, xAY,Lag (AY = 1,..,n, Lag = 1,…,n, AY + Lag < n + 2), the goal of a stochastic loss reserve model is to predict the distribution of outcomes, XAY,Lag (AY + Lag > n +1), and sums of losses such as , 2 2 n n AY Lag AY Lag n AY X . This paper will propose a set of diagnostics to test the predictive distribution and illustrate the use of these diagnostics on American insurer data as reported to the National Association of Insurance Commissioners (NAIC). The data will consist of incremental paid losses for the commercial automobile line of insurance. This data will come from a database containing both the original loss triangles and the outcomes. This database will contain data for hundreds of American insurers, and it will be posted on the Casualty Actuarial Society (CAS) website for all researchers to access. The retrospective tests are performed on the familiar stochastic loss reserve model, the bootstrap chain ladder overdispersed Poisson model. The paper will also perform the retrospective tests on a model proposed by the authors. The authors’ model will assume that the incremental paid losses have a Tweedie distribution, with the expected loss ratio and calendar year trend parameters following an AR(1) time series model. The model will be a hierarchical Bayesian model with the posterior distribution of parameters being estimated by Markov‐Chain Monte‐Carlo (MCMC) methods.
