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Anticipated backward stochastic differential equations on Markov chains

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  • Lu, Wen
  • Ren, Yong

Abstract

In this paper, we deal with a class of anticipated backward stochastic differential equations related to finite state, continuous time Markov chains. The adapted solution of those equations as well as a scalar comparison theorem will be established.

Suggested Citation

  • Lu, Wen & Ren, Yong, 2013. "Anticipated backward stochastic differential equations on Markov chains," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1711-1719.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:7:p:1711-1719
    DOI: 10.1016/j.spl.2013.03.022
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
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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. Xiong, Yafang & Xu, Xiaoming, 2020. "Anticipated backward stochastic differential equations with left-Lipschitz coefficient," Statistics & Probability Letters, Elsevier, vol. 163(C).
    3. Wu, Hao & Li, Xuefeng, 2021. "Converse comparison theorems for multidimensional anticipated backward stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 168(C).

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