Reflected BSDEs with optional barrier in a general filtration

We consider reflected backward stochastic differential equations, with two barriers, defined on probability spaces equipped with filtration satisfying only the usual assumptions of right-continuity and completeness. As for barriers, we assume that there are càdlàg processes of class D that are completely separated. We prove the existence and uniqueness of solutions for an integrable final condition and an integrable monotone generator. An application to the zero-sum Dynkin game is given.

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Predictable solution for reflected BSDEs when the obstacle is not right-continuous

Random Operators and Stochastic Equations ◽

10.1515/rose-2020-2045 ◽

2020 ◽

Vol 28 (4) ◽

pp. 269-279

Author(s):

Mohamed Marzougue ◽

Mohamed El Otmani

Keyword(s):

Brownian Motion ◽

Differential Equations ◽

Stochastic Differential Equations ◽

Existence And Uniqueness ◽

Random Measure ◽

Backward Stochastic Differential Equations ◽

Poisson Random Measure ◽

One Dimensional ◽

General Filtration ◽

Reflected Bsdes

AbstractIn the present paper, we consider reflected backward stochastic differential equations when the reflecting obstacle is not necessarily right-continuous in a general filtration that supports a one-dimensional Brownian motion and an independent Poisson random measure. We prove the existence and uniqueness of a predictable solution for such equations under the stochastic Lipschitz coefficient by using the predictable Mertens decomposition.

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A general comparison theorem for reflected BSDEs

Statistics & Probability Letters ◽

10.1016/j.spl.2021.109058 ◽

2021 ◽

pp. 109058

Author(s):

Mun-Chol Kim ◽

Hun O

Keyword(s):

Comparison Theorem ◽

Reflected Bsdes

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Solving the double barrier reflected BSDEs via penalization method

Statistics & Probability Letters ◽

10.1016/j.spl.2015.12.003 ◽

2016 ◽

Vol 110 ◽

pp. 74-83 ◽

Cited By ~ 2

Author(s):

Min Li ◽

Yufeng Shi

Keyword(s):

Double Barrier ◽

Penalization Method ◽

Reflected Bsdes

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Double-barriers-reflected BSDEs with jumps and viscosity solutions of parabolic integrodifferential PDEs

Journal of Applied Mathematics and Stochastic Analysis ◽

10.1155/jamsa.2005.37 ◽

2005 ◽

Vol 2005 (1) ◽

pp. 37-53 ◽

Cited By ~ 8

Author(s):

N. Harraj ◽

Y. Ouknine ◽

I. Turpin

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Viscosity Solutions ◽

Backward Stochastic Differential Equations ◽

Probabilistic Interpretation ◽

Reflected Bsdes

We give a probabilistic interpretation of the viscosity solutions of parabolic integrodifferential partial equations with two obstacles via the solutions of forward-backward stochastic differential equations with jumps.

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