Robust simulation of environmental policies using the DICE model

Integrated assessment models that combine geophysics and economics features are often used to evaluate environmental economic policies. In these models, there are often profound uncertainties and Monte Carlo simulations are often used to evaluate the policies. Generally, the simulation approach requires that the distribution of the uncertain parameters are clearly specified. In this paper, we adopt the widely used multivariate normal distribution to model the uncertain parameters. However, we assume that the mean vector and covariance matrix of the distribution are within some ambiguity sets. We propose a change-of-measure technique to derive the simulation results for any mean vector and covariance matrix in the sets without actually simulating them. We then show how to find the worst case performance for all mean vectors and covariance matrices in the ambiguity sets by solving a sequence of convex problems. This performance provides a robust evaluation of the policies. We test our algorithm on a famous environmental economic model, known as the DICE model, and obtain some insightful and interesting results.