Correlation and Aggregate Loss Distributions With An Emphasis On The Iman-Conover Method

Motivation. The CAS Research Working Party on Correlation and Dependencies Among All Risk Sources has been charged to “lay the theoretical and experimental foundation for quantifying variability when data is limited, estimating the nature and magnitude of dependence relationships, and generating aggregate distributions that integrate these disparate risk sources.” Method. The Iman-Conover method represents a straight forward yet powerful approach to working with dependent random variables. We explain the theory behind the method and give a detailed step-by-step algorithm to implement it. We discuss various extensions to the method, and give detailed examples showing how it can be used to solve real world actuarial problems. We also summarize pertinent facts from the theory of univariate and multivariate aggregate loss distributions, with a focus on the use of moment generating functions. Finally we explain how Vitale’s Theorem provides a sound theoretical foundation to the Iman-Conover method. Availability. The software used to generate the paper’s examples is available at http://www.mynl.com/wp.