Correlations and Copulas for Decision and Risk Analysis

• Published in: Management science Vol. 45; no. 2; pp. 208 - 224
• Main Authors: Clemen, Robert T, Reilly, Terence
• Format: Journal Article
• Language: English
• Published: Linthicum, MD INFORMS 01.02.1999; Institute for Operations Research and the Management Sciences
• Series: Management Science
• Subjects: Accuracy; Airlines; Applied sciences; Approximation; Copula functions; copulas; Correlation analysis; Correlations; Decision analysis; decision analysis process; Decision theory; Decision theory. Utility theory; Distribution theory; Exact sciences and technology; Kendall's \tau; Kendall's τ; Mathematics; measures of dependence; Modeling; Multivariate analysis; multivariate normal copula; Normal distribution; Operational research and scientific management; Operational research. Management science; Probabilities; Probability; Probability and statistics; Probability theory and stochastic processes; Random variables; Risk; Risk analysis; Risk assessment; Risk management; Sciences and techniques of general use; Sensitivity analysis; Spearman's \rho; Spearman's ρ; Standard deviation; Studies; Uncertainty; United States > US; Dependence; Marginal distribution; Gaussian distribution; Multivariate distribution; Probabilistic model; Decision analysis; Risk analysis; Joint distribution
• ISSN: 0025-1909; 1526-5501
• DOI: 10.1287/mnsc.45.2.208

The construction of a probabilistic model is a key step in most decision and risk analyses. Typically this is done by defining a joint distribution in terms of marginal and conditional distributions for the model's random variables. We describe an alternative approach that uses a copula to construct joint distributions and pairwise correlations to incorporate dependence among the variables. The approach is designed specifically to permit the use of an expert's subjective judgments of marginal distributions and correlations. The copula that underlies the multivariate normal distribution provides the basis for modeling dependence, but arbitrary marginals are allowed. We discuss how correlations can be assessed using techniques that are familiar to decision analysts, and we report the results of an empirical study of the accuracy of the assessment methods. The approach is demonstrated in the context of a simple example, including a study of the sensitivity of the results to the assessed correlations.