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Backward stochastic differential equations with two reflecting barriers and continuous with quadratic growth coefficient

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  • Bahlali, Khaled
  • Hamadène, SaI¨d
  • Mezerdi, Brahim

Abstract

We deal with backward stochastic differential equations with two reflecting barriers and a continuous coefficient which is, first, linear growth in (y,z) and then quadratic growth with respect to z. In both cases we show the existence of a maximal solution.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:115:y:2005:i:7:p:1107-1129
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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. 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.
    3. 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:

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    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. Essaky, E.H. & Hassani, M. & Ouknine, Y., 2015. "Stochastic quadratic BSDE with two RCLL obstacles," Stochastic Processes and their Applications, Elsevier, vol. 125(6), pages 2147-2189.
    4. Zheng, Shiqiu & Zhou, Shengwu, 2008. "A generalized existence theorem of reflected BSDEs with double obstacles," Statistics & Probability Letters, Elsevier, vol. 78(5), pages 528-536, April.
    5. 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.
    6. 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.
    7. Li, Min & Shi, Yufeng, 2016. "Solving the double barrier reflected BSDEs via penalization method," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 74-83.

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