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Generalized Feynman-Kac Formula under volatility uncertainty

Author

Listed:
  • Bahar Akhtari
  • Francesca Biagini
  • Andrea Mazzon
  • Katharina Oberpriller

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 $G$-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.

Suggested Citation

  • Bahar Akhtari & Francesca Biagini & Andrea Mazzon & Katharina Oberpriller, 2020. "Generalized Feynman-Kac Formula under volatility uncertainty," Papers 2012.08163, arXiv.org, revised Nov 2022.
    • Handle: RePEc:arx:papers:2012.08163
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    References listed on IDEAS

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    1. Tolulope Fadina & Ariel Neufeld & Thorsten Schmidt, 2018. "Affine processes under parameter uncertainty," Papers 1806.02912, arXiv.org, revised Mar 2019.
    2. Soner, H. Mete & Touzi, Nizar & Zhang, Jianfeng, 2011. "Martingale representation theorem for the G-expectation," Stochastic Processes and their Applications, Elsevier, vol. 121(2), pages 265-287, February.
    3. Hu, Mingshang & Ji, Shaolin & Peng, Shige & Song, Yongsheng, 2014. "Comparison theorem, Feynman–Kac formula and Girsanov transformation for BSDEs driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 124(2), pages 1170-1195.
    4. Francesca Biagini & Katharina Oberpriller, 2020. "Reduced-form setting under model uncertainty with non-linear affine processes," Papers 2006.14307, arXiv.org, revised Jun 2020.
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