Aggregate claim analysis estimates the total random claim for a book of insurance product line by studying possible aggregate claim distributions. Such distributions are probability distributions of the total dollar amount of loss under one or more insurance policies. They combine the separate effects of the underlying frequency and severity distributions.

The main problem is how to calculate aggregate claims for a book of business which is the union of disjoint classes of business, each of which has an aggregate distribution. The classes of business are NOT assumed to be independent.

This study addresses the evaluation of the aggregate claim without assuming independent individual claims. A non-traditional approach is proposed which estimates the expected random sum based on a stochastic model of individual claims. By using the contingent claim analysis, the expected random sum is approximated by solving a partial differential equation. Numerical examples and applications are also discussed in the study.