English

Second order backward SDE with random terminal time

Probability 2022-02-14 v2 Optimization and Control

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).

Keywords

Cite

@article{arxiv.1802.02260,
  title  = {Second order backward SDE with random terminal time},
  author = {Yiqing Lin and Zhenjie Ren and Nizar Touzi and Junjian Yang},
  journal= {arXiv preprint arXiv:1802.02260},
  year   = {2022}
}
R2 v1 2026-06-23T00:13:58.335Z