A Method to Calculate Aggregate Excess Loss Distributions

The purpose of the paper is to develop a method of calculating the aggregate loss distribution of excess claims based on a formula described in the book Risk Theory by Beard, Pentikainenen, and Pesonen. This formula requires that the claim frequency distribution satisfy a certain recursive relationship. The first part of the paper shows that a claim frequency distributions of excess claims derived from a claim frequency distribution satisfying the recursive relationship also has the recursive property. The second part describes a simple Pascal program that implements the calculation of aggregate loss distributions using these formulas. Reinsurance Research - Loss Distributions, Size of