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A ℂ0,1-functional Itô’s formula and its applications in mathematical finance

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  • Bouchard, Bruno
  • Loeper, Grégoire
  • Tan, Xiaolu

Abstract

Using Dupire’s notion of vertical derivative, we provide a functional (path-dependent) extension of the Itô’s formula of Gozzi and Russo (2006) that applies to C0,1-functions of continuous weak Dirichlet processes. It is motivated and illustrated by its applications to the hedging or superhedging problems of path-dependent options in mathematical finance, in particular in the case of model uncertainty. In this context, we also prove a new regularity result for the vertical derivative of candidate solutions to a class of path-depend PDEs, using an approximation argument which seems to be original and of own interest.

Suggested Citation

  • Bouchard, Bruno & Loeper, Grégoire & Tan, Xiaolu, 2022. "A ℂ0,1-functional Itô’s formula and its applications in mathematical finance," Stochastic Processes and their Applications, Elsevier, vol. 148(C), pages 299-323.
    • Handle: RePEc:eee:spapps:v:148:y:2022:i:c:p:299-323
    DOI: 10.1016/j.spa.2022.02.010
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    References listed on IDEAS

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    1. Jianfeng Zhang & Jia Zhuo, 2014. "Monotone schemes for fully nonlinear parabolic path dependent PDEs," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 1-23.
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