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Quadratic BSDEs with convex generators and unbounded terminal conditions
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  • Published: 01 August 2007

Quadratic BSDEs with convex generators and unbounded terminal conditions

  • Philippe Briand1 &
  • Ying Hu1 

Probability Theory and Related Fields volume 141, pages 543–567 (2008)Cite this article

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Abstract

In Briand and Hu (Probab Theory Relat Fields 136(4):604–618, 2006), the authors proved an existence result for BSDEs with quadratic generators with respect to the variable z and with unbounded terminal conditions. However, no uniqueness result was stated in that work. The main goal of this paper is to fill this gap. In order to obtain a comparison theorem for this kind of BSDEs, we assume that the generator is convex with respect to the variable z. Under this assumption of convexity, we are also able to prove a stability result in the spirit of the a priori estimates stated in Karoui et al. (Math Finance 7(1):1–71, 1997). With these tools in hands, we can derive the nonlinear Feynman–Kac formula in this context.

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Authors and Affiliations

  1. IRMAR, Université Rennes 1, 35 042, Rennes Cedex, France

    Philippe Briand & Ying Hu

Authors
  1. Philippe Briand
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  2. Ying Hu
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Correspondence to Philippe Briand.

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Briand, P., Hu, Y. Quadratic BSDEs with convex generators and unbounded terminal conditions. Probab. Theory Relat. Fields 141, 543–567 (2008). https://doi.org/10.1007/s00440-007-0093-y

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  • Received: 15 March 2007

  • Revised: 27 June 2007

  • Published: 01 August 2007

  • Issue Date: July 2008

  • DOI: https://doi.org/10.1007/s00440-007-0093-y

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Mathematics Subject Classification (2000)

  • 60H10
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