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

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  • Monia Karouf

    (Gabès University)

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.

Suggested Citation

  • Monia Karouf, 2019. "Reflected and Doubly Reflected Backward Stochastic Differential Equations with Time-Delayed Generators," Journal of Theoretical Probability, Springer, vol. 32(1), pages 216-248, March.
    • Handle: RePEc:spr:jotpro:v:32:y:2019:i:1:d:10.1007_s10959-018-0829-x
    DOI: 10.1007/s10959-018-0829-x
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    References listed on IDEAS

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    5. dos Reis, Gonçalo & Réveillac, Anthony & Zhang, Jianing, 2011. "FBSDEs with time delayed generators: Lp-solutions, differentiability, representation formulas and path regularity," Stochastic Processes and their Applications, Elsevier, vol. 121(9), pages 2114-2150, September.
    6. Li Chen & Jianhui Huang, 2015. "Stochastic Maximum Principle for Controlled Backward Delayed System via Advanced Stochastic Differential Equation," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 1112-1135, December.
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    8. Delong, Lukasz & Imkeller, Peter, 2010. "On Malliavin's differentiability of BSDEs with time delayed generators driven by Brownian motions and Poisson random measures," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1748-1775, August.
    9. Quenez, Marie-Claire & Sulem, Agnès, 2013. "BSDEs with jumps, optimization and applications to dynamic risk measures," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3328-3357.
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