Modeling uncertainty of expert elicitation for use in risk-based optimization

Capital budgeting optimization models, used in a broad number of fields, require certain and uncertain parameters. Often times, elicited subject matter expert (SME) opinion is used as a parameter estimate, which does not always yield perfect information or correspond to a single value. Because of the uncertainty of the elicitation, the unknown true value of a parameter can be modeled as a random variable from a to-be-determined distribution. We estimate a univariate distribution using four different approaches, the Beta and Gaussian distributions, a standard Gaussian Kernel estimate, and an exponential epi-spline. We also capture dependencies within the parameters through three multivariate approaches: the multivariate Gaussian distribution, the multivariate Kernel and the multivariate exponential epi-spline. This is the first three-dimensional application of the latter. Sampling from the densities, we generate scenarios and implement a superquantile risk-based, capital budgeting optimization model. Numerical experiments contrast the differences between estimators, as well as their effects on an optimal solution. Our findings demonstrate that naively averaging the SME observations for use in optimization, rather than incorporating uncertainty, results in an overly optimistic portfolio. The flexibility of the exponential epi-spline estimator to fuse soft information with observed data produces reasonable density functions for univariate and multivariate random variables. Including a decision-maker’s risk-averseness through risk-based optimization delivers conservative results while incorporating the uncertainty of unknown parameters. We demonstrate a 20% improvement for this specific case when using our approach as opposed to the naive method.