Dynamic Frailty Count Process in Insurance: A Unified Framework for Estimation, Pricing, and Forecasting
研究了保险中风险因子随时间变化且不可观测的计数过程，提出一个统一框架进行估计、定价和预测，并通过车险定价实例展示了模型捕捉索赔历史非线性影响的能力。
Abstract We study count processes in insurance, in which the underlying risk factor is time varying and unobservable. The factor follows an autoregressive gamma process, and the resulting model generalizes the static Poisson‐Gamma model and allows for closed form expression for the posterior Bayes (linear or nonlinear) premium. Moreover, the estimation and forecasting can be conducted within the same framework in a rather efficient way. An example of automobile insurance pricing illustrates the ability of the model to capture the duration dependent, nonlinear impact of past claims on future ones and the improvement of the Bayes pricing method compared to the linear credibility approach.