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Backward SDEs with superquadratic growth
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  • Published: 25 February 2010

Backward SDEs with superquadratic growth

  • Freddy Delbaen1,
  • Ying Hu2 &
  • Xiaobo Bao1 

Probability Theory and Related Fields volume 150, pages 145–192 (2011)Cite this article

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  • 53 Citations

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Abstract

In this paper, we discuss the solvability of backward stochastic differential equations (BSDEs) with superquadratic generators. We first prove that given a superquadratic generator, there exists a bounded terminal value, such that the associated BSDE does not admit any bounded solution. On the other hand, we prove that if the superquadratic BSDE admits a bounded solution, then there exist infinitely many bounded solutions for this BSDE. Finally, we prove the existence of a solution for Markovian BSDEs where the terminal value is a bounded continuous function of a forward stochastic differential equation.

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Authors and Affiliations

  1. Department of Mathematics, ETH Zürich, 8092, Zurich, Switzerland

    Freddy Delbaen & Xiaobo Bao

  2. IRMAR, Université Rennes 1, 35042, Rennes Cedex, France

    Ying Hu

Authors
  1. Freddy Delbaen
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  2. Ying Hu
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  3. Xiaobo Bao
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Corresponding author

Correspondence to Ying Hu.

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Delbaen, F., Hu, Y. & Bao, X. Backward SDEs with superquadratic growth. Probab. Theory Relat. Fields 150, 145–192 (2011). https://doi.org/10.1007/s00440-010-0271-1

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  • Received: 19 February 2009

  • Revised: 18 January 2010

  • Published: 25 February 2010

  • Issue Date: June 2011

  • DOI: https://doi.org/10.1007/s00440-010-0271-1

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Mathematics Subject Classification (2000)

  • 60H10
  • 93E20
  • 91B30
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