Generalized Feynman-Kac Formula under volatility uncertainty

Abstract

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 in [9], 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.

Robust deep hedging

“…Our paper relates to a rich stream of literature motivated by parameter uncertainty, dating back to Avellaneda et al (1995), Wilmott and Oztukel (1998), and Fouque and Ren (2014). More recent contributions are Cohen and Tegnér (2017), Barnett et al (2020), Aksamit et al (2020), Cheridito et al (2017), Akthari et al (2020). In the context of option pricing and efficient hedging, Bouchard et al (2015), Hou and Ob lój (2018) developed approaches respecting an ambiguity set of possible underlying probability measures and Acciaio et al (2016), Beiglböck et al (2013), Cox and Ob lój (2011), Dolinsky and Soner (2014), Lütkebohmert and Sester (2019), Neufeld and Sester (2021b) introduced approaches to entirely model-free option pricing and to model-free super-replication.…”