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Pré-Publication, Document De Travail Année : 2019

Second order backward SDE with random terminal time

Résumé

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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Dates et versions

hal-02293001 , version 1 (20-09-2019)

Identifiants

  • HAL Id : hal-02293001 , version 1

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Yiqing Lin, Zhenjie Ren, Nizar Touzi, Junjian Yang. Second order backward SDE with random terminal time. 2019. ⟨hal-02293001⟩
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