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Reflected and Doubly Reflected Backward Stochastic Differential Equations with Time-Delayed Generators

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Abstract

In this paper, we study reflected backward stochastic differential equations with two reflecting barriers and time-delayed generators (delay RBSDEs for short). We consider the case of Brownian noise as well as the case of Brownian and Poisson noise. For both cases, we show the existence and uniqueness of the solution and give a comparison theorem.

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Acknowledgements

The author expresses his gratitude to Professor Monique Pontier for her careful reading and helpful suggestions. Here we address special thanks to Professor Anthony Reveillac for his invaluable comments and advice on this paper.

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Authors and Affiliations

  1. Higher Institute of Applied Sciences and Technologies of Gabès & LR17ES11, Gabès University, Gabès, Tunisia

    Monia Karouf

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  1. Monia Karouf
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Correspondence to Monia Karouf.

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Karouf, M. Reflected and Doubly Reflected Backward Stochastic Differential Equations with Time-Delayed Generators. J Theor Probab 32, 216–248 (2019). https://doi.org/10.1007/s10959-018-0829-x

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  • DOI: https://doi.org/10.1007/s10959-018-0829-x

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