Modeling Insurance Claims using a Compound Distribution

A typical model for insurance risk, the so-called collective risk model, treats the aggregate loss as having a compound distribution with two main components one characterizing the arrival of claims and another describing the severity (or size) of loss resulting from the occurrence of a claim. We review a collection of loss distributions and present methods that can be used to assess the goodness-of-fit of the claim size distribution. The collective risk model is often used in health insurance and in general insurance, whenever the main risk components are the number of insurance claims and the amount of the claims. It can also be used for modeling other non-insurance product risks, such as credit and operational risk.