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Second order backward SDE with random terminal time

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1802.02260.pdf (419.8Kb)
Date
2018-02
Publisher city
Paris
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Publishing date
02-2018
Collection title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Dewey
Probabilités et mathématiques appliquées
Sujet
Backward SDE; second order backward SDE; quasi-sure stochastic analysis; random horizon
URI
https://basepub.dauphine.fr/handle/123456789/19862
Collections
  • CEREMADE : Publications
Metadata
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Author
Lin, Yiqing
89626 Centre de Mathématiques Appliquées - Ecole Polytechnique [CMAP]
Ren, Zhenjie
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Touzi, Nizar
89626 Centre de Mathématiques Appliquées - Ecole Polytechnique [CMAP]
Yang, Junjian
441966 Fakultät für Mathematik und Geoinformation [Wien]
Type
Document de travail / Working paper
Item number of pages
36
Abstract (EN)
Backward stochastic differential equations extend the martingale representation theorem to the nonlinear setting. This can be seen as path-dependent counterpart of the extension from the heat equation to fully nonlinear parabolic equations in the Markov setting. This paper extends such a nonlinear representation to the context where the random variable of interest is measurable with respect to the information at a finite stopping time. We provide a complete wellposedness theory which covers the semilinear case (backward SDE), the semilinear case with obstacle (reflected backward SDE), and the fully nonlinear case (second order backward SDE).

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