Quantifying Distributional Model Risk via Optimal Transport

TL;DR

This paper introduces a method to quantify the impact of model misspecification on expected values using optimal transport distances, providing bounds that are applicable to a wide range of stochastic processes and risk analysis scenarios.

Contribution

It develops a general framework for bounding expectations under model uncertainty using optimal transport distances, including Wasserstein, with applications to risk analysis and non-parametric tolerance estimation.

Findings

Provides a flexible methodology for model risk quantification.

Demonstrates applications in path-dependent stochastic processes.

Includes non-parametric estimation techniques for tolerance regions.

Abstract

This paper deals with the problem of quantifying the impact of model misspecification when computing general expected values of interest. The methodology that we propose is applicable in great generality, in particular, we provide examples involving path dependent expectations of stochastic processes. Our approach consists in computing bounds for the expectation of interest regardless of the probability measure used, as long as the measure lies within a prescribed tolerance measured in terms of a flexible class of distances from a suitable baseline model. These distances, based on optimal transportation between probability measures, include Wasserstein's distances as particular cases. The proposed methodology is well-suited for risk analysis, as we demonstrate with a number of applications. We also discuss how to estimate the tolerance region non-parametrically using Skorokhod-type embeddings in some of these applications.