Bayesian premium of a credibility model based on a heterogeneous SETINAR(2,1) process.

In this paper, we propose a new credibility model based on heterogeneous integer-valued self-exciting threshold autoregressive time series, in which the SETINAR(2,1) process is used to fit the claim numbers of policyholders for consecutive periods, and the unobservable heterogeneity is assumed to follow Gamma distribution. We obtain the Bayesian pricing formula for the proposed model and present some numerical examples to illustrate how the claim history affects the future premiums. We also apply the proposed model to a real panel dataset from the Wisconsin Local Government Property Insurance Fund. By comparing with some existing models, we find that our model can exploit the past information more efficiently and has better predictive performance. [ABSTRACT FROM AUTHOR]