Reflected backward stochastic differential equations with two optional barriers

Tomasz Klimsiak; Maurycy Rzymowski; Leszek Słomiński

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arXiv · 1810.07969

Reflected backward stochastic differential equations with two optional barriers

Tomasz Klimsiak·Maurycy Rzymowski·Leszek Słomiński

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Abstract

We consider reflected backward stochastic differential equations with two general optional barriers. The solutions to these equations have the so-called regulated trajectories, i.e trajectories with left and right finite limits. We prove the existence and uniqueness of $\mathbb L^p$ solutions, $p\geq 1$, and show that the solutions may be approximated by a modified penalization method.

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Tomasz Klimsiak, Maurycy Rzymowski, Leszek Słomiński. 2018-10-18. Reflected backward stochastic differential equations with two optional barriers. https://arxiv.org/abs/1810.07969

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