When preparing for the SOA Exam C or CAS Exam MAS-I, understanding compound Poisson processes is essential because these exams test your ability to model aggregate losses—a fundamental skill in actuarial science. The compound Poisson process elegantly captures the randomness in both the number of claims and their sizes, making it a cornerstone for modeling insurance claims and risk.

At its core, a compound Poisson process models the total claim amount as the sum of a random number of individual claims. The number of claims follows a Poisson distribution, reflecting the frequency of claims over a fixed period, while each claim size is an independent random variable drawn from the same distribution, representing severity. This setup aligns well with real-world insurance scenarios, where both how many claims happen and how big they are vary unpredictably.