Generalized Feynman–Kac formula under volatility uncertainty

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...

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Bibliographic Details
Published in:Stochastic processes and their applications 2023-12, Vol.166, p.104083, Article 104083
Main Authors: Akhtari, Bahar, Biagini, Francesca, Mazzon, Andrea, Oberpriller, Katharina
Format: Article
Language:English
Subjects:
Feynmac–Kac formula
Nonlinear PDEs
Sublinear conditional expectation
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Summary: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.
ISSN:0304-4149
DOI:10.1016/j.spa.2022.12.003