Premium
Dynamic Frailty Count Process in Insurance: A Unified Framework for Estimation, Pricing, and Forecasting
Author(s) -
Lu Yang
Publication year - 2018
Publication title -
journal of risk and insurance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.055
H-Index - 63
eISSN - 1539-6975
pISSN - 0022-4367
DOI - 10.1111/jori.12190
Subject(s) - unobservable , cox process , econometrics , count data , gamma process , poisson distribution , credibility , autoregressive model , compound poisson process , bayes' theorem , poisson process , economics , estimation , computer science , mathematics , bayesian probability , statistics , management , political science , law
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.