Second order backward sde with random terminal time

Yiqing Lin, Zhenjie Ren, Nizar Touzi, Junjian Yang

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Article number99
Pages (from-to)1-43
Number of pages43
JournalElectronic Journal of Probability
StatePublished - 2020


  • Backward SDE
  • Quasi-sure stochastic analysis
  • Random horizon
  • Second order backward SDE

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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