A combined integer-valued autoregressive process with actuarial applications

Abstract

This paper proposes a modification of a combined integer-valued autoregressive (CINAR) process based on binomial thinning, which is instrumental in modelling higher-order dependence between the number of claims in an insurance portfolio. The modified CINAR process is more general and enjoys stationarity and flexibility in higher-order serial dependence modelling. Two actuarial applications of the proposed process in risk theory and credibility model are explored. As an application to risk theory, we derive the distribution of aggregate claims under a discrete-time collective risk model and examine the effect of high-order dependence on the tail-related risk measures of the aggregate claims. Next, we apply the modified CINAR process to account for the unobserved gamma heterogeneity in determining the dynamics of the predictive credibility premium. A real data analysis shows that our approach provides a superior pattern to the predictive premium calculation when compared to the outcomes of several alternative models.