Copulas and Correlations in Risk Analysis Modeling. Robert T. Clemen, Fuqua School of Business, Duke University, Durham, NC 27708
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 from probability assessment in decision and risk analysis. The approach is demonstrated in the context of two examples. The first is a standard textbook decision-analysis model. The second is an application involving the aggregation of experts’ assessed probability distributions.