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Wellposedness of Second Order Backward SDEs

Zhang, Jianfeng; Touzi, Nizar; Soner, Halil Mete (2012), Wellposedness of Second Order Backward SDEs, Probability Theory and Related Fields, 153, 1-2, p. 149-190. http://dx.doi.org/10.1007/s00440-011-0342-y

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Type
Article accepté pour publication ou publié
Date
2012
Journal name
Probability Theory and Related Fields
Volume
153
Number
1-2
Publisher
Springer
Pages
149-190
Publication identifier
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Author(s)
Zhang, Jianfeng

Touzi, Nizar
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Soner, Halil Mete
Abstract (EN)
We provide an existence and uniqueness theory for an extension of backward SDEs to the second order. While standard Backward SDEs are naturally connected to semilinear PDEs, our second order extension is connected to fully nonlinear PDEs, as suggested in [4]. In particular, we provide a fully nonlinear extension of the Feynman-Kac formula. Unlike [4], the alternative formulation of this paper insists that the equation must hold under a non-dominated family of mutually singular probability measures. The key argument is a stochastic representation, suggested by the optimal control interpretation, and analyzed in the accompanying paper [17].
Subjects / Keywords
non-dominated family of mutually singular measures; Backward SDEs; viscosity solutions for second order PDEs