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A converse comparison theorem for anticipated BSDEs and related non-linear expectations

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  • Yang, Zhe
  • Elliott, Robert J.
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    Abstract

    The converse comparison theorem has received much attention in the theory of backward stochastic differential equations (BSDEs). However, no such theorem has been proved for anticipated BSDEs. In this paper, we derive a converse comparison theorem by first giving an existence and uniqueness theorem for adapted solutions of anticipated BSDEs with a stopping time and then related to (f,δ)-expectations induced by anticipated BSDEs.

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 123 (2013)
    Issue (Month): 2 ()
    Pages: 275-299

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    Handle: RePEc:eee:spapps:v:123:y:2013:i:2:p:275-299

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    Related research

    Keywords: Anticipated BSDEs; Stopping times; (f; δ)-expectations; Converse comparison theorem;

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    1. Chen, Zengjing & Peng, Shige, 2000. "A general downcrossing inequality for g-martingales," Statistics & Probability Letters, Elsevier, vol. 46(2), pages 169-175, January.
    2. Rosazza Gianin, Emanuela, 2006. "Risk measures via g-expectations," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 19-34, August.
    3. 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.
    4. Jiang, Long, 2005. "Converse comparison theorems for backward stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 71(2), pages 173-183, February.
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