Abstract
Abstract Risk theory models describe the uncertainty associated with the claims recorded by an insurance company for losses incurred by its policy holders. The claims frequency and the claims severity are two important components of these models. This article centers on models for the frequency of losses. Even if an insurance company were able to maintain the exact same portfolio of policies over time, the number of claims recorded would still vary from year to year. Such natural fluctuations are modeled through the claim number random variable. Over time, claim counts evolve according to a stochastic process: the claim number process. While other sections discuss specific claim number processes in greater detail, the general features are given here.
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