Wellposedness of Second Order Backward SDEs

2010/03/31 by H. Mete Soner, Nizar Touzi, Jianfeng Zhang · 2 citations
Mathematics · #math.PR #msc:60H10 #msc:60H30

paper · pdf

published as Probability Theory and Related Fields, 153, 149--190, (2012) · 36 pages

arxiv created 2012/02/26 · arxiv updated 2013/06/18

Abstract

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 by Cheridito et.al. In particular, we provide a fully nonlinear extension of the Feynman-Kac formula. Unlike the earlier papers, 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 our accompanying paper

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