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Penalization method for reflected backward stochastic differential equations with one r.c.l.l. barrier

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  • Lepeltier, J.-P.
  • Xu, M.

Abstract

In this paper, we consider BSDEs with a Lipschitz coefficient reflected on one discontinuous (r.c.l.l.) barrier. We prove the convergence of the solutions of the penalized equations to the solution of the RBSDE.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:75:y:2005:i:1:p:58-66
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Gechun Liang & Wei Wei & Zhen Wu & Zhenda Xu, 2024. "Recursive Optimal Stopping with Poisson Stopping Constraints," Papers 2407.17975, arXiv.org.
    2. 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.
    3. Ren, Yong & Hu, Lanying, 2007. "Reflected backward stochastic differential equations driven by Lévy processes," Statistics & Probability Letters, Elsevier, vol. 77(15), pages 1559-1566, September.
    4. Falkowski, Adrian & Słomiński, Leszek, 2020. "Backward stochastic differential equations with two barriers and generalized reflection," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 4746-4765.
    5. Klimsiak, Tomasz & Rzymowski, Maurycy & Słomiński, Leszek, 2019. "Reflected BSDEs with regulated trajectories," Stochastic Processes and their Applications, Elsevier, vol. 129(4), pages 1153-1184.
    6. Tahir Choulli & Ella Elazkany & Mich`ele Vanmaele, 2024. "The second-order Esscher martingale densities for continuous-time market models," Papers 2407.03960, arXiv.org.
    7. Marzougue, Mohamed, 2021. "Monotonic limit theorem for BSDEs with regulated trajectories," Statistics & Probability Letters, Elsevier, vol. 176(C).
    8. Mohamed Otmani, 2009. "Reflected BSDE Driven by a Lévy Process," Journal of Theoretical Probability, Springer, vol. 22(3), pages 601-619, September.
    9. Li, Hanwu & Peng, Shige & Soumana Hima, Abdoulaye, 2018. "Reflected Solutions of BSDEs Driven by $\textit{G}$-Brownian Motion," Center for Mathematical Economics Working Papers 590, Center for Mathematical Economics, Bielefeld University.
    10. Zhou, Qing & Ren, Yong, 2012. "Reflected backward stochastic differential equations with time delayed generators," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 979-990.
    11. Irina Penner & Anthony Réveillac, 2015. "Risk measures for processes and BSDEs," Finance and Stochastics, Springer, vol. 19(1), pages 23-66, January.
    12. Neda Esmaeeli & Peter Imkeller, 2015. "American Options with Asymmetric Information and Reflected BSDE," Papers 1505.05046, arXiv.org, revised Aug 2017.
    13. Klimsiak, Tomasz & Rozkosz, Andrzej & Słomiński, Leszek, 2015. "Reflected BSDEs in time-dependent convex regions," Stochastic Processes and their Applications, Elsevier, vol. 125(2), pages 571-596.
    14. Shige Peng & Mingyu Xu, 2006. "Reflected BSDE with a Constraint and a New Doob-Meyer Nonlinear Decomposition," Papers math/0611869, arXiv.org, revised Jul 2008.
    15. Kim, Mun-Chol & O, Hun, 2021. "A general comparison theorem for reflected BSDEs," Statistics & Probability Letters, Elsevier, vol. 173(C).
    16. Li, Hanwu & Peng, Shige, 2020. "Reflected backward stochastic differential equation driven by G-Brownian motion with an upper obstacle," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6556-6579.
    17. Choukroun, Sébastien & Cosso, Andrea & Pham, Huyên, 2015. "Reflected BSDEs with nonpositive jumps, and controller-and-stopper games," Stochastic Processes and their Applications, Elsevier, vol. 125(2), pages 597-633.
    18. Roxana Dumitrescu & Romuald Elie & Wissal Sabbagh & Chao Zhou, 2017. "A new Mertens decomposition of $\mathscr{Y}^{g,\xi}$-submartingale systems. Application to BSDEs with weak constraints at stopping times," Papers 1708.05957, arXiv.org, revised May 2023.

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