Open Access
Translator Disclaimer
2020 Second order backward SDE with random terminal time
Yiqing Lin, Zhenjie Ren, Nizar Touzi, Junjian Yang
Electron. J. Probab. 25: 1-43 (2020). DOI: 10.1214/20-EJP498

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).

Citation

Download Citation

Yiqing Lin. Zhenjie Ren. Nizar Touzi. Junjian Yang. "Second order backward SDE with random terminal time." Electron. J. Probab. 25 1 - 43, 2020. https://doi.org/10.1214/20-EJP498

Information

Received: 8 May 2018; Accepted: 23 July 2020; Published: 2020
First available in Project Euclid: 18 August 2020

zbMATH: 07252731
MathSciNet: MR4136479
Digital Object Identifier: 10.1214/20-EJP498

Subjects:
Primary: 60H10 , 60H30

Keywords: Backward SDE , quasi-sure stochastic analysis , random horizon , second order backward SDE

JOURNAL ARTICLE
43 PAGES


SHARE
Vol.25 • 2020
Back to Top