Minimal Supersolutions of Convex BSDEs and Robust Extensions

We study minimal supersolutions of convex BSDEs - related to Peng's g-expectation - which can be seen as a superhedging functionals. We prove existence, uniqueness, monotone convergence, Fatou's Lemma and lower semicontinuity of our functional.

Unlike usual BSDE methods, based on fixed point theorems, the existence rely on compactness methods. We illustrate this approach by presenting how it can be applied in the problem of exponential utility maximisation.

Our approach can further be extended to address problems of robustification, where the Brownian motion in the superhedging problem is yet subject to volatility uncertainty. We will present some results and ideas about this second ongoing work.

This talk is based on joint works with Gregor Heyne and Michael Kupper.