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Second order backward SDE with random terminal time

Lin, Yiqing; Ren, Zhenjie; Touzi, Nizar; Yang, Junjian (2020), Second order backward SDE with random terminal time, Electronic Journal of Probability, 25, p. 1-43. 10.1214/20-EJP498

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Type
Article accepté pour publication ou publié
Date
2020
Journal name
Electronic Journal of Probability
Volume
25
Publisher
Institute of Mathematical Statistics
Published in
Paris
Pages
1-43
Publication identifier
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Author(s)
Lin, Yiqing
Centre de Mathématiques Appliquées - Ecole Polytechnique [CMAP]
Ren, Zhenjie
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Touzi, Nizar
Centre de Mathématiques Appliquées - Ecole Polytechnique [CMAP]
Yang, Junjian
Fakultät für Mathematik und Geoinformation [Wien] [TU Wien]
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).
Subjects / Keywords
Backward SDE; second order backward SDE; quasi-sure stochastic analysis; random horizon