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Mathematics Colloquium

Jan Obloj
University of Oxford

Title: Data driven robustness and uncertainty sensitivity analysis
Date: Friday, September 18, 2020
Place and Time: Zoom, 3:35-4:25 pm

Abstract. In this talk, I will showcase how methods from optimal transport and distributionally robust optimisation allow to capture and quantify sensitivity to model uncertainty for a myriad of problems. We consider a generic stochastic optimisation problem. This could be a mean-variance or a utility maximisation portfolio allocation problem, an optimised certainty equivalent or a risk measure computation, a certification problem, a standard regression or a deep learning problem. At the heart of the optimisation is a probability measure, or a model, which describes the system. It could come from data, simulation or a modelling effort but there is always a degree of uncertainty about it. We take a non-parametric approach and capture model uncertainty using Wasserstein balls around the postulated measure. Our main results provide explicit formulae for the first order correction to both the value function and the optimiser. We further extend our results to optimisation under linear constraints. Our sensitivity analysis of the distributionally robust optimisation problems finds applications in statistics, machine learning, mathematical finance and uncertainty quantification. I will discuss several examples in the talk including: option pricing, portfolio selection, risk assessments, square-root LASSO and square-root Ridge regression and measures of NN architecture robustness wrt to adversarial data. Talk based on joint works with Daniel Bartl, Samuel Drapeau and Johannes Wiesel.