Sensitivity of causal distributionally robust optimization

Understand

We study the causal distributionally robust optimization (DRO) in both discrete- and continuous- time settings.

• The framework captures model uncertainty, with potential models penalized in function of their adapted Wasserstein distance to a given reference model.
• Strength of the penalty is controlled using a real-valued parameter which, in the special case of an indicator penalty, is simply the radius of the uncertainty ball.
• Our main results derive the first-order sensitivity of the value of causal DRO with respect to the penalization parameter, i.e., we compute the sensitivity to model uncertainty.