Distributionally robust risk evaluation with a causality constraint and structural information

The choice of the underlying probability measure is crucial in measuring risk or other objectives, but it presents a challenge for decision-makers (DMs) to find an expressive yet tractable reference measure. One simple option is to use the empirical measure on a sample dataset, but this choice is prone to model misspecification due to small sample sizes or blurred observations. Additionally, time-series data can pose further difficulties for modeling, creating another source of misspecification. This paper aims to provide a robust framework for risk evaluation with temporal data. Since Knight (1921) clarified the subtle difference between risk and model uncertainty (misspecification), several methodologies have been developed to incorporate robustness.