Title: Distributionally Robust Performance Analysis with Applications to Mine Valuation and Risk
Description: We consider several problems motivated by issues faced in the mining industry. In recent years, it has become clear that mines have substantial tail risk in the form of environmental disasters, and this tail risk is not incorporated into common pricing and risk models. However, data sets of the extremal climate behavior that drive this risk are very small, and generally inadequate for properly estimating the tail behavior. We propose a data-driven methodology that comes up with reasonable worst-case scenarios, given the data size constraints, and we incorporate this into a real options based model for the valuation of mines. We propose several different iterations of the model, to allow the end-user to choose the degree to which they wish to specify the financial consequences of the disaster scenario. Next, in order to perform a risk analysis on a portfolio of mines, we propose a method of estimating the correlation structure of high-dimensional max-stable processes. Using the techniques of (Liu Et al, 2017) to map the relationship between normal correlations and max-stable correlations, we can then use techniques inspired by (Bickel et al, 2008, Liu et al, 2014, Rothman et al, 2009) to estimate the underlying correlation matrix, while preserving a sparse, positive-definite structure.

The correlation matrices are then used in the calculation of model-robust risk metrics (VaR, CVAR) using the the Sample-Out-of-Sample methodology (Blanchet and Kang, 2017). We conclude with several new techniques that were developed in the field of robust performance analysis, that while not directly applied to mining, were motivated by our studies into distributionally robust optimization in order to address these problems.