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Filtration Consistent Nonlinear Expectations

In: Recent Developments In Mathematical Finance

Author

Listed:
  • François Coquet

    (IRMAR, U.M.R. C.N.R.S. 6625, Campus de Beaulieu, Université Rennes 1, 35042 Rennes, Cédex, France)

  • Ying Hu

    (IRMAR, U.M.R. C.N.R.S. 6625, Campus de Beaulieu, Université Rennes 1, 35042 Rennes, Cédex, France)

  • Jean Mémin

    (IRMAR, U.M.R. C.N.R.S. 6625, Campus de Beaulieu, Université Rennes 1, 35042 Rennes, Cédex, France)

  • Shige Peng

    (Department of Mathematics, Shangdong University, Jinan 250100, China)

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 martingales. 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.

Suggested Citation

  • François Coquet & Ying Hu & Jean Mémin & Shige Peng, 2001. "Filtration Consistent Nonlinear Expectations," World Scientific Book Chapters, in: Jiongmin Yong (ed.), Recent Developments In Mathematical Finance, chapter 9, pages 99-116, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812799579_0009
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