WKB Approximation for the Sum of Two Correlated Lognormal Random Variables

In this paper we apply the idea of the WKB method to derive an effective single lognormal approximation for the probability distribution of the sum of two correlated lognormal variables. An approximate probability distribution of the sum is determined in closed form, and illustrative numerical examples are presented to demonstrate the validity and accuracy of the approximate distribution. Our analysis shows that the proposed method is able to provide a simple, efficient and accurate approximation to the probability distribution of the sum of two correlated lognormal variables. We also discuss how this new approach can be straightforwardly extended to study the sum of N lognormals