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}
}