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Convexity bounds for BSDE solutions, with applications to indifference valuation
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  • Published: 11 March 2010

Convexity bounds for BSDE solutions, with applications to indifference valuation

  • Christoph Frei1,
  • Semyon Malamud2 &
  • Martin Schweizer3 

Probability Theory and Related Fields volume 150, pages 219–255 (2011)Cite this article

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  • 4 Citations

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Abstract

We consider backward stochastic differential equations (BSDEs) with a particular quadratic generator and study the behaviour of their solutions when the probability measure is changed, the filtration is shrunk, or the underlying probability space is transformed. Our main results are upper bounds for the solutions of the original BSDEs in terms of solutions to other BSDEs which are easier to solve. We illustrate our results by applying them to exponential utility indifference valuation in a multidimensional Itô process setting.

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Author information

Authors and Affiliations

  1. CMAP, École Polytechnique, 91128, Palaiseau Cedex, France

    Christoph Frei

  2. Swiss Finance Institute, EPFL, 1015, Lausanne, Switzerland

    Semyon Malamud

  3. Department of Mathematics, ETH Zurich, 8092, Zurich, Switzerland

    Martin Schweizer

Authors
  1. Christoph Frei
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  2. Semyon Malamud
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  3. Martin Schweizer
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Corresponding author

Correspondence to Martin Schweizer.

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Frei, C., Malamud, S. & Schweizer, M. Convexity bounds for BSDE solutions, with applications to indifference valuation. Probab. Theory Relat. Fields 150, 219–255 (2011). https://doi.org/10.1007/s00440-010-0273-z

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  • Received: 18 March 2009

  • Revised: 10 January 2010

  • Published: 11 March 2010

  • Issue Date: June 2011

  • DOI: https://doi.org/10.1007/s00440-010-0273-z

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Keywords

  • Quadratic BSDE
  • Convexity bounds
  • Symmetrisation
  • Indifference valuation
  • Exponential utility

Mathematics Subject Classification (2000)

  • 60H10
  • 91B28
  • 60G35
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