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A $C^{0,1}$-functional It\^o's formula and its applications in mathematical finance

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  • Bruno Bouchard
  • Gr'egoire Loeper
  • Xiaolu Tan

Abstract

Using Dupire's notion of vertical derivative, we provide a functional (path-dependent) extension of the It\^o's formula of Gozzi and Russo (2006) that applies to C^{0,1}-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

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  • Bruno Bouchard & Gr'egoire Loeper & Xiaolu Tan, 2021. "A $C^{0,1}$-functional It\^o's formula and its applications in mathematical finance," Papers 2101.03759, arXiv.org.
    • Handle: RePEc:arx:papers:2101.03759
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    References listed on IDEAS

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    1. Ariel Neufeld & Marcel Nutz, 2012. "Superreplication under Volatility Uncertainty for Measurable Claims," Papers 1208.6486, arXiv.org, revised Apr 2013.
    2. 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.
    3. Bruno Bouchard & Jean-François Chassagneux, 2016. "Fundamentals and Advanced Techniques in Derivatives Hedging," Post-Print hal-01348864, HAL.
    4. Gozzi, Fausto & Russo, Francesco, 2006. "Weak Dirichlet processes with a stochastic control perspective," Stochastic Processes and their Applications, Elsevier, vol. 116(11), pages 1563-1583, November.
    5. Bruno Bouchard & Xiaolu Tan, 2019. "Understanding the dual formulation for the hedging of path-dependent options with price impact," Working Papers hal-02398881, HAL.
    6. Bandini, Elena & Russo, Francesco, 2017. "Weak Dirichlet processes with jumps," Stochastic Processes and their Applications, Elsevier, vol. 127(12), pages 4139-4189.
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