Actuarial Science Seminar: Modeling insurance claims using integer-valued autoregressive processes

Integer-valued autoregressive of order one (INAR(1)) processes are used in modeling non-life insurance claims. This type of model is suitable for claims counting processes with lag-one dependence. Three applications of INAR(1) model in insurance claims are discussed in this talk. Firstly, an INAR(1) process with dynamic heterogeneity is introduced to model the random fluctuations and correlations from year to year. The application of this model to automobile insurance is presented. Secondly, a Poisson INAR(1) process is proposed to model the number of (unclosed) incurred but not reported (IBNR) claims. Model properties and parameter estimations are discussed. Finally, a compound model based on the Poisson INAR(1) counting process (for closed IBNR claims) is studied for the total claim payments. Maximum likelihood techniques are applied for estimating model parameters. Simulation studies are used to illustrate the estimation results and to examine their accuracy. Predictions based on proposed models are also discussed.
This is a joint work with Ting Zhang, Yang Bai and Jinwan Kim.