Generalized Feynman–Kac formula under volatility uncertainty

Akhtari, Bahar; Biagini, Francesca ; Mazzon, Andrea and Oberpriller, Katharina (2023): Generalized Feynman–Kac formula under volatility uncertainty. In: Stochastic Processes and their Applications, Vol. 166, 104083

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 et al. (2014), where the Lipschitz continuity of some functionals is assumed which is not necessarily satisfied in our setting. In particular, we show that the G-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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Workgroup Financial Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 03044149
• Language: English