Second order backward SDE with random terminal time

Understand

Backward stochastic differential equations extend the martingale representation theorem to the nonlinear setting.

• This can be seen as path-dependent counterpart of the extension from the heat equation to fully nonlinear parabolic equations in the Markov setting.
• This paper extends such a nonlinear representation to the context where the random variable of interest is measurable with respect to the information at a finite stopping time.
• We provide a complete wellposedness theory which covers the semilinear case (backward SDE), the semilinear case with obstacle (reflected backward SDE), and the fully nonlinear case (second order backward SDE).