The Fatou Closedness under Model Uncertainty

TL;DR

This paper characterizes Fatou closedness for certain convex sets under model uncertainty, with applications to robust asset pricing and risk measures, extending classical results to non-dominated probability frameworks.

Contribution

It introduces a new characterization of Fatou closedness for weakly closed convex sets under non-dominated probability measures, advancing the theory of robust financial models.

Findings

Provides a characterization of Fatou closedness in non-dominated settings

Extends the Fundamental Theorem of Asset Pricing to model uncertainty

Offers dual representations of convex risk measures under uncertainty

Abstract

We provide a characterization in terms of Fatou closedness for weakly closed monotone convex sets in the space of $\mathcal{P}$-quasisure bounded random variables, where $\mathcal{P}$ is a (possibly non-dominated) class of probability measures. Applications of our results lie within robust versions the Fundamental Theorem of Asset Pricing or dual representation of convex risk measures.