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Lp solutions to backward stochastic differential equations with discontinuous generators

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  • Tian, Dejian
  • Jiang, Long
  • Shi, Xuejun

Abstract

In this paper, we deal with the Lp(p>1) solutions to one dimensional backward stochastic differential equations (BSDEs) with discontinuous generators. We obtain an existence theorem of Lp solutions for BSDEs whose generators satisfy a kind of discontinuous condition in y and are uniformly continuous in z.

Suggested Citation

  • Tian, Dejian & Jiang, Long & Shi, Xuejun, 2013. "Lp solutions to backward stochastic differential equations with discontinuous generators," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 503-510.
  • Handle: RePEc:eee:stapro:v:83:y:2013:i:2:p:503-510
    DOI: 10.1016/j.spl.2012.10.026
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    References listed on IDEAS

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    1. Jia, Guangyan, 2008. "A class of backward stochastic differential equations with discontinuous coefficients," Statistics & Probability Letters, Elsevier, vol. 78(3), pages 231-237, February.
    2. Mao, Xuerong, 1995. "Adapted solutions of backward stochastic differential equations with non-Lipschitz coefficients," Stochastic Processes and their Applications, Elsevier, vol. 58(2), pages 281-292, August.
    3. 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.
    4. 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.
    5. Briand, Ph. & Delyon, B. & Hu, Y. & Pardoux, E. & Stoica, L., 2003. "Lp solutions of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 109-129, November.
    6. Fan, ShengJun & Jiang, Long & Tian, DeJian, 2011. "One-dimensional BSDEs with finite and infinite time horizons," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 427-440, March.
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