Open Access
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


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).


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Yiqing Lin. Zhenjie Ren. Nizar Touzi. Junjian Yang. "Second order backward SDE with random terminal time." Electron. J. Probab. 25 1 - 43, 2020.


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

Primary: 60H10 , 60H30

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

Vol.25 • 2020
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