Adapted Wasserstein Distances and Stability in Mathematical Finance

Understand

Assume that an agent models a financial asset through a measure Q with the goal to price / hedge some derivative or optimize some expected utility.

• Even if the model Q is chosen in the most skilful and sophisticated way, she is left with the possibility that Q does not provide an "exact" description of reality.
• This leads us to the following question: will the hedge still be somewhat meaningful for models in the proximity of Q? If we measure proximity with the usual Wasserstein distance (say), the answer is NO.
• Models which are similar w.r.t.