Risk measures based on weak optimal transport

Understand

In this paper, we study convex risk measures with weak optimal transport penalties.

• In a first step, we show that these risk measures allow for an explicit representation via a nonlinear transform of the loss function.
• In a second step, we discuss computational aspects related to the nonlinear transform as well as approximations of the risk measures using, for example, neural networks.
• Our setup comprises a variety of examples, such as classical optimal transport penalties, parametric families of models, uncertainty on path spaces, moment constrains, and martingale constraints.