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A comonotonic theorem for BSDEs

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  • Chen, Zengjing
  • Kulperger, Reg
  • Wei, Gang

Abstract

Pardoux and Peng (Systems Control Lett. 14 (1990) 55) introduced a class of nonlinear backward stochastic differential equations (BSDEs). According to Pardoux and Peng's theorem, the solution of this type of BSDE consists of a pair of adapted processes, say (y,z). Since then, many researchers have been exploring the properties of this pair solution (y,z), especially the properties of the first part y. In this paper, we shall explore the properties of the second part z. A comonotonic theorem with respect to z is obtained. As an application of this theorem, we prove an integral representation theorem of the solution of BSDEs.

Suggested Citation

  • Chen, Zengjing & Kulperger, Reg & Wei, Gang, 2005. "A comonotonic theorem for BSDEs," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 41-54, January.
    • Handle: RePEc:eee:spapps:v:115:y:2005:i:1:p:41-54
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    References listed on IDEAS

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    1. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
    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.
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    Cited by:

    1. He, Kun & Hu, Mingshang & Chen, Zengjing, 2009. "The relationship between risk measures and choquet expectations in the framework of g-expectations," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 508-512, February.
    2. Chen, Zengjing & Kulperger, Reg, 2006. "Minimax pricing and Choquet pricing," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 518-528, June.
    3. Chen, Zengjing & Kulperger, Reg, 2005. "Inequalities for upper and lower probabilities," Statistics & Probability Letters, Elsevier, vol. 73(3), pages 233-241, July.
    4. Ryota Iijima & Akitada Kasahara, 2016. "Gradual Adjustment and Equilibrium Uniqueness under Noisy Monitoring," ISER Discussion Paper 0965, Institute of Social and Economic Research, Osaka University.
    5. Ji, Shaolin & Shi, Xiaomin, 2018. "Reaching goals under ambiguity: Continuous-time optimal portfolio selection," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 63-69.

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