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The adapted solutions and comparison theorem for anticipated backward stochastic differential equations with Poisson jumps under the weak conditions

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  • Tu, Shuheng
  • Hao, Wu
  • Chen, Jing

Abstract

This paper considers a class of anticipated backward stochastic differential equations with Poisson jumps (ABSDEJs). We prove the existence and uniqueness result of adapted solutions for such ABSDEJs under some weak assumption conditions. We also derive some comparison theorems by applying Girsanov Theorem.

Suggested Citation

  • Tu, Shuheng & Hao, Wu & Chen, Jing, 2017. "The adapted solutions and comparison theorem for anticipated backward stochastic differential equations with Poisson jumps under the weak conditions," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 7-17.
    • Handle: RePEc:eee:stapro:v:126:y:2017:i:c:p:7-17
    DOI: 10.1016/j.spl.2017.02.022
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    References listed on IDEAS

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    1. Rong, Situ, 1997. "On solutions of backward stochastic differential equations with jumps and applications," Stochastic Processes and their Applications, Elsevier, vol. 66(2), pages 209-236, March.
    2. Royer, Manuela, 2006. "Backward stochastic differential equations with jumps and related non-linear expectations," Stochastic Processes and their Applications, Elsevier, vol. 116(10), pages 1358-1376, October.
    3. Jia, Guangyan, 2009. "Some uniqueness results for one-dimensional BSDEs with uniformly continuous coefficients," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 436-441, February.
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