A parametric approach to the estimation of convex risk functionals based on Wasserstein distance

Understand

In this paper, we explore a static setting for the assessment of risk in the context of mathematical finance and actuarial science that takes into account model uncertainty in the distribution of a possibly infinite-dimensional risk factor.

• We allow for perturbations around a baseline model, measured via Wasserstein distance, and we investigate to which extent this form of probabilistic imprecision can be parametrized.
• The aim is to come up with a convex risk functional that incorporates a sefety margin with respect to nonparametric uncertainty and still can be approximated through parametrized models.
• The particular form of the parametrization allows us to develop a numerical method, based on neural networks, which gives both the value of the risk functional and the optimal perturbation of the reference measure.