Mathematics – Probability
Scientific paper
2010-03-31
Mathematics
Probability
36 pages
Scientific paper
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
Soner Halil Mete
Touzi Nizar
Zhang Jianfeng
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