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Reflected BSDEs and mixed game problem

Author

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  • Hamadène, S.
  • Lepeltier, J. -P.

Abstract

Under smooth assumptions and notably the Isaacs's condition on the Hamiltonian, we prove the existence of a saddle-point for the "mixed" zero-sum stochastic differential game with payoffThe main tool is the notion of double barrier reflected backward SDEs.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:85:y:2000:i:2:p:177-188
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    Cited by:

    1. Bayraktar, Erhan & Yao, Song, 2015. "Doubly reflected BSDEs with integrable parameters and related Dynkin games," Stochastic Processes and their Applications, Elsevier, vol. 125(12), pages 4489-4542.
    2. Hamadène, S. & Wang, H., 2009. "BSDEs with two RCLL reflecting obstacles driven by Brownian motion and Poisson measure and a related mixed zero-sum game," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 2881-2912, September.
    3. Said Hamadène & Monique Jeanblanc, 2007. "On the Starting and Stopping Problem: Application in Reversible Investments," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 182-192, February.
    4. Huang, Zongyuan & Lepeltier, Jean-Pierre & Wu, Zhen, 2010. "Reflected forward-backward stochastic differential equations with continuous monotone coefficients," Statistics & Probability Letters, Elsevier, vol. 80(21-22), pages 1569-1576, November.
    5. Ekren, Ibrahim, 2017. "Viscosity solutions of obstacle problems for fully nonlinear path-dependent PDEs," Stochastic Processes and their Applications, Elsevier, vol. 127(12), pages 3966-3996.
    6. Roman Gayduk & Sergey Nadtochiy, 2020. "Control-Stopping Games for Market Microstructure and Beyond," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1289-1317, November.
    7. 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.
    8. Erhan Bayraktar & Song Yao, 2015. "On the Robust Dynkin Game," Papers 1506.09184, arXiv.org, revised Sep 2016.
    9. Roxana Dumitrescu & Marie-Claire Quenez & Agn`es Sulem, 2015. "Game options in an imperfect market with default," Papers 1511.09041, arXiv.org, revised Jul 2017.
    10. Hamadène, Said & Zhang, Jianfeng, 2010. "Switching problem and related system of reflected backward SDEs," Stochastic Processes and their Applications, Elsevier, vol. 120(4), pages 403-426, April.
    11. Zhou, Qing & Ren, Yong, 2012. "Reflected backward stochastic differential equations with time delayed generators," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 979-990.
    12. Lin, Qian, 2009. "A class of backward doubly stochastic differential equations with non-Lipschitz coefficients," Statistics & Probability Letters, Elsevier, vol. 79(20), pages 2223-2229, October.
    13. Fan, Xiliang & Ren, Yong & Zhu, Dongjin, 2010. "A note on the doubly reflected backward stochastic differential equations driven by a Lévy process," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 690-696, April.
    14. Miryana Grigorova & Marie-Claire Quenez & Yuan Peng, 2023. "Non-linear non-zero-sum Dynkin games with Bermudan strategies," Papers 2311.01086, arXiv.org.
    15. Bahlali, Khaled & Hamadène, SaI¨d & Mezerdi, Brahim, 2005. "Backward stochastic differential equations with two reflecting barriers and continuous with quadratic growth coefficient," Stochastic Processes and their Applications, Elsevier, vol. 115(7), pages 1107-1129, July.
    16. Klimsiak, Tomasz, 2021. "Non-semimartingale solutions of reflected BSDEs and applications to Dynkin games," Stochastic Processes and their Applications, Elsevier, vol. 134(C), pages 208-239.
    17. Grigorova, Miryana & Imkeller, Peter & Quenez, Marie-Claire & Ouknine, Youssef, 2018. "Doubly Reflected BSDEs and $\mathcal{E}$$^ƒ$-Dynkin games: beyond the right-continuous case," Center for Mathematical Economics Working Papers 598, Center for Mathematical Economics, Bielefeld University.
    18. Roman Gayduk & Sergey Nadtochiy, 2017. "Control-stopping Games for Market Microstructure and Beyond," Papers 1708.00506, arXiv.org, revised Mar 2019.
    19. Jingnan Wang & Ralf Korn, 2020. "Numerical Algorithms for Reflected Anticipated Backward Stochastic Differential Equations with Two Obstacles and Default Risk," Risks, MDPI, vol. 8(3), pages 1-30, July.
    20. Benjamin Jourdain & Michel Vellekoop, 2009. "Regularity of the Exercise Boundary for American Put Options on Assets with Discrete Dividends," Working Papers hal-00436327, HAL.
    21. Giovanni Mottola, 2014. "Generalized Dynkin game of switching type representation for defaultable claims in presence of contingent CSA," Papers 1410.0594, arXiv.org, revised Jan 2015.
    22. 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.
    23. Nie, Tianyang & Rutkowski, Marek, 2014. "Multi-player stopping games with redistribution of payoffs and BSDEs with oblique reflection," Stochastic Processes and their Applications, Elsevier, vol. 124(8), pages 2672-2698.

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