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Abstract
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This is a joint work with Jianfeng Zhang and Mete Soner. 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. In particular, we provide a fully nonlinear extension of the Feynman-Kac formula. The 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. |
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