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Filtration-consistent nonlinear expectations and related g-expectations
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  • Published: May 2002

Filtration-consistent nonlinear expectations and related g-expectations

  • François Coquet1,
  • Ying Hu1,
  • Jean Mémin1 &
  • …
  • Shige Peng2 

Probability Theory and Related Fields volume 123, pages 1–27 (2002)Cite this article

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Abstract

 From a general definition of nonlinear expectations, viewed as operators preserving monotonicity and constants, we derive, under rather general assumptions, the notions of conditional nonlinear expectation and nonlinear martingale. We prove that any such nonlinear martingale can be represented as the solution of a backward stochastic equation, and in particular admits continuous paths. In other words, it is a g-martingale.

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Authors and Affiliations

  1. IRMAR, Université de Rennes 1 35042 Rennes Cédex, France. e-mail: Francois.Coquet@univ-rennes1.fr, , , , , , FR

    François Coquet, Ying Hu & Jean Mémin

  2. Department of Mathematics, Shandong University, 250100 Jinan, China., , , , , , CN

    Shige Peng

Authors
  1. François Coquet
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  2. Ying Hu
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  3. Jean Mémin
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  4. Shige Peng
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Additional information

Received: 2 February 2000 / Revised version: 1 June 2001 / Published online: 13 May 2002

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Cite this article

Coquet, F., Hu, Y., Mémin, J. et al. Filtration-consistent nonlinear expectations and related g-expectations. Probab Theory Relat Fields 123, 1–27 (2002). https://doi.org/10.1007/s004400100172

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  • Issue Date: May 2002

  • DOI: https://doi.org/10.1007/s004400100172

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Keywords

  • General Assumption
  • General Definition
  • Stochastic Equation
  • Continuous Path
  • Nonlinear Expectation
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