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Mean-field backward stochastic differential equations in general probability spaces

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  • Lu, Wen
  • Ren, Yong
  • Hu, Lanying

Abstract

In this paper, we deal with a class of mean-field backward stochastic differential equations in continuous time with an arbitrary filtered probability space. We prove the existence and uniqueness of a solution for those equations with strengthened Lipschitz assumption. A comparison theorem is also established.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:263:y:2015:i:c:p:1-11
    DOI: 10.1016/j.amc.2015.04.014
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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.
    2. Cohen, Samuel N., 2012. "Representing filtration consistent nonlinear expectations as g-expectations in general probability spaces," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1601-1626.
    3. Li, Zhi & Luo, Jiaowan, 2012. "Mean-field reflected backward stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1961-1968.
    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, January.
    5. Cohen, Samuel N. & Elliott, Robert J., 2010. "A general theory of finite state Backward Stochastic Difference Equations," Stochastic Processes and their Applications, Elsevier, vol. 120(4), pages 442-466, April.
    6. Samuel N. Cohen & Robert J. Elliott, 2008. "Comparisons for backward stochastic differential equations on Markov chains and related no-arbitrage conditions," Papers 0810.0055, arXiv.org, revised Jan 2010.
    7. Lu, Wen & Ren, Yong, 2013. "Anticipated backward stochastic differential equations on Markov chains," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1711-1719.
    8. Buckdahn, Rainer & Li, Juan & Peng, Shige, 2009. "Mean-field backward stochastic differential equations and related partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3133-3154, October.
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    Cited by:

    1. Maximilien Germain & Huyên Pham & Xavier Warin, 2021. "A level-set approach to the control of state-constrained McKean-Vlasov equations: application to renewable energy storage and portfolio selection," Working Papers hal-03498263, HAL.

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