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Reflected backward stochastic differential equations with time delayed generators

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  • Zhou, Qing
  • Ren, Yong

Abstract

In this paper, we establish the existence and uniqueness of the solution for a class of reflected backward stochastic differential equations with time delayed generator (RBSDEs with time delayed generator, in short) for a sufficiently small Lipschitz constant of the generator.

Suggested Citation

  • Zhou, Qing & Ren, Yong, 2012. "Reflected backward stochastic differential equations with time delayed generators," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 979-990.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:5:p:979-990
    DOI: 10.1016/j.spl.2012.02.012
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    References listed on IDEAS

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    1. El-Karoui, N. & Hamadène, S., 2003. "BSDEs and risk-sensitive control, zero-sum and nonzero-sum game problems of stochastic functional differential equations," Stochastic Processes and their Applications, Elsevier, vol. 107(1), pages 145-169, September.
    2. Lepeltier, J.-P. & Xu, M., 2005. "Penalization method for reflected backward stochastic differential equations with one r.c.l.l. barrier," Statistics & Probability Letters, Elsevier, vol. 75(1), pages 58-66, November.
    3. 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.
    4. Hamadène, S. & Lepeltier, J. -P., 2000. "Reflected BSDEs and mixed game problem," Stochastic Processes and their Applications, Elsevier, vol. 85(2), pages 177-188, February.
    5. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    6. 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.
    7. Łukasz Delong, 2010. "Applications of backward stochastic differential equations to insurance and finance," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 21, pages 11-26.
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    Cited by:

    1. 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.
    2. Luo, Peng, 2020. "Reflected BSDEs with time-delayed generators and nonlinear resistance," Statistics & Probability Letters, Elsevier, vol. 163(C).

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