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Mean-field reflected backward stochastic differential equations

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  • Li, Zhi
  • Luo, Jiaowan

Abstract

In this paper, mean-field reflected backward stochastic differential equations (MF-RBSDEs, for short) are introduced and studied. We prove the existence and uniqueness of solutions for MF-RBSDEs under the Lipschitz condition by a fixed point argument. Under monotone assumptions for coefficients, we show a comparison theorem for MF-RBSDEs. We finally get an existence and a comparison theorem of the minimal solution when the coefficients are continuous, non-decreasing in y′ and have a linear growth.

Suggested Citation

  • Li, Zhi & Luo, Jiaowan, 2012. "Mean-field reflected backward stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1961-1968.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:11:p:1961-1968
    DOI: 10.1016/j.spl.2012.06.018
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    References listed on IDEAS

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    1. Ahmed, N. U. & Ding, X., 1995. "A semilinear Mckean-Vlasov stochastic evolution equation in Hilbert space," Stochastic Processes and their Applications, Elsevier, vol. 60(1), pages 65-85, November.
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    Cited by:

    1. Lu, Wen & Ren, Yong & Hu, Lanying, 2015. "Mean-field backward stochastic differential equations in general probability spaces," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 1-11.
    2. Zong, Gaofeng & Chen, Zengjing, 2013. "Harnack inequality for mean-field stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1424-1432.

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