Generalized Feynman-Kac Formula under volatility uncertainty
Abstract
In this paper we provide a generalization of a Feynmac-Kac formula under volatility uncertainty in presence of a linear term in the PDE due to 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 show that the -conditional expectation of a discounted payoff is a viscosity solution of a nonlinear PDE. In applications, this permits to calculate such a sublinear expectation in a computationally efficient way.
Cite
@article{arxiv.2012.08163,
title = {Generalized Feynman-Kac Formula under volatility uncertainty},
author = {Bahar Akhtari and Francesca Biagini and Andrea Mazzon and Katharina Oberpriller},
journal= {arXiv preprint arXiv:2012.08163},
year = {2022}
}
Comments
35 pages, 3 figures