Understanding the dual formulation for the hedging of path-dependent options with price impact

Bruno Bouchard () and Xiaolu Tan
Additional contact information
Bruno Bouchard: CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique
Xiaolu Tan: CUHK - The Chinese University of Hong Kong [Hong Kong]

Post-Print from HAL

Abstract: We consider a general path-dependent version of the hedging problem with price impact of Bouchard et al. (2019), in which a dual formulation for the super-hedging price is obtained by means of PDE arguments, in a Markovian setting and under strong regularity conditions. Using only probabilistic arguments, we prove, in a path-dependent setting and under weak regularity conditions, that any solution to this dual problem actually allows one to construct explicitly a perfect hedging portfolio. From a pure probabilistic point of view, our approach also allows one to exhibit solutions to a specific class of second order forward backward stochastic differential equations, in the sense of Cheridito et al. (2007). Existence of a solution to the dual optimal control problem is also addressed in particular settings. As a by-product of our arguments, we prove a version of Itô's Lemma for path-dependent functionals that are only C^{0,1} in the sense of Dupire.

Date: 2022-06
Note: View the original document on HAL open archive server: https://hal.science/hal-02398881v2
References: View references in EconPapers View complete reference list from CitEc
Citations:

Published in The Annals of Applied Probability, 2022, 32 (3), pp.1705-1733. ⟨10.1214/21-AAP1719⟩

Downloads: (external link)
https://hal.science/hal-02398881v2/document (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-02398881

DOI: 10.1214/21-AAP1719

Access Statistics for this paper

More papers in Post-Print from HAL
Bibliographic data for series maintained by CCSD ().