Wellposedness of Second Order Backward SDEs

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

36 pages

References in corpus (5)

• A theoretical framework for the pricing of contingent claims in the presence of model uncertainty
• Martingale Representation Theorem for the G-expectation
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• Dual formulation of second order target problems
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Cited by in corpus (3)

• Weak Approximation of G-Expectations
• Backward stochastic differential equations under super linear G-expectation and associated Hamilton-Jacobi-Bellman equations
• A variational representation and large deviations for functionals of G-Brownian motion