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Anticipated backward stochastic differential equations with non-Lipschitz coefficients

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  • Wu, Hao
  • Wang, Wenyuan
  • Ren, Jie

Abstract

This paper deals with a class of anticipated backward stochastic differential equations. We extend results of Peng and Yang (2009) to the case in which the generator satisfies non-Lipschitz condition. The existence and uniqueness of solutions for anticipated backward stochastic differential equations as well as a comparison theorem are obtained. The existence and uniqueness of Lp(p>2) solutions for anticipated backward stochastic differential equations are also studied.

Suggested Citation

  • Wu, Hao & Wang, Wenyuan & Ren, Jie, 2012. "Anticipated backward stochastic differential equations with non-Lipschitz coefficients," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 672-682.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:3:p:672-682
    DOI: 10.1016/j.spl.2011.12.008
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    References listed on IDEAS

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    1. Fan, ShengJun & Liu, DeQun, 2010. "A class of BSDE with integrable parameters," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 2024-2031, December.
    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. 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.
    4. Lepeltier, J. P. & San Martin, J., 1997. "Backward stochastic differential equations with continuous coefficient," Statistics & Probability Letters, Elsevier, vol. 32(4), pages 425-430, April.
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    Cited by:

    1. Lu, Wen & Ren, Yong, 2013. "Anticipated backward stochastic differential equations on Markov chains," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1711-1719.
    2. Yu, Xianye, 2019. "Non-Lipschitz anticipated backward stochastic differential equations driven by fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 155(C), pages 1-1.
    3. Xiong, Yafang & Xu, Xiaoming, 2020. "Anticipated backward stochastic differential equations with left-Lipschitz coefficient," Statistics & Probability Letters, Elsevier, vol. 163(C).

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