Generalized Feynman-Kac Formula under volatility uncertainty

Bahar Akhtari, Francesca Biagini, Andrea Mazzon, Katharina Oberpriller

Published 2020-12-15, updated 2021-07-19Version 2

In this paper we provide a generalization of the Feynmac-Kac formula under volatility uncertainty in presence of discounting. We state our result under different hypothesis with respect to the derivation given by Hu, Ji, Peng and Song (Comparison theorem, Feynman-Kac formula and Girsanov transformation for BSDEs driven by G-Brownian motion, Stochastic Processes and their Application, 124 (2)), where the Lipschitz continuity of some functionals is assumed which is not necessarily satisfied in our setting. In particular, we obtain the $G$-conditional expectation of a discounted payoff as the limit of $C^{1,2}$ solutions of some regularized PDEs, for different kinds of convergence. In applications, this permits to approximate such a sublinear expectation in a computationally efficient way.