Abstract
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).
Original language | English (US) |
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Article number | 99 |
Pages (from-to) | 1-43 |
Number of pages | 43 |
Journal | Electronic Journal of Probability |
Volume | 25 |
DOIs | |
State | Published - 2020 |
Keywords
- Backward SDE
- Quasi-sure stochastic analysis
- Random horizon
- Second order backward SDE
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty