A Non-simulation Based Method for Inducing Pearson's Correlation between Input Random Variables

Abstract

Several previously published papers have cited the need to include correlation in risk-analysis models. In particular, a landmark paper published by Philip Lurie and Matthew Goldberg presented a methodology for inducing Pearson's correlation between input/independent random variables. The one subject, absent from the paper, was a methodology for finding the optimal applied correlation matrix given a desired outcome correlation. Since the publishing of the Lurie-Goldberg paper, there has been continuing discussion on its implementation; however, there has not been any presentation of an optimization algorithm that does not involve the use of computing-heavy simulations. This paper reviews the general methodology used by Lurie and Goldberg (along with its predecessor papers) and presents a non-simulation approach to finding the optimal input correlation matrix, given a set of marginal distributions and a desired correlation matrix.