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Quadratic Semimartingale BSDEs Under an Exponential Moments Condition

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Séminaire de Probabilités XLIV

Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 2046))

Abstract

In the present article we provide existence, uniqueness and stability results under an exponential moments condition for quadratic semimartingale backward stochastic differential equations (BSDEs) having convex generators. We show that the martingale part of the BSDE solution defines a true change of measure and provide an example which demonstrates that pointwise convergence of the drivers is not sufficient to guarantee a stability result within our framework.

AMS Classification: 60H10

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Acknowledgements

This chapter was originally published within the PhD thesis “Utility Maximization and Quadratic BSDEs under Exponential Moments” by Markus Mocha, Humboldt University Berlin, 2012. With kind permission of the author.

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Authors and Affiliations

  1. Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany

    Markus Mocha

  2. Department of Mathematics, Imperial College, SW7 2AZ, London, UK

    Nicholas Westray

Authors
  1. Markus Mocha
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  2. Nicholas Westray
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Correspondence to Markus Mocha .

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Editors and Affiliations

  1. , Laboratoire de Mathématiques, Université de Versailles-St-Quentin, avenue des États-Unis 45, Versailles, 78035, France

    Catherine Donati-Martin

  2. IECN, Campus scientifique, BP 239, Nancy-Université, INRIA, Vandoeuvre-lès-Nancy, 54506, France

    Antoine Lejay

  3. Laboratoire de Mathématiques, Université de Versailles-St-Quentin, avenue des Etats-Unis 45, Versailles, 78035, France

    Alain Rouault

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Mocha, M., Westray, N. (2012). Quadratic Semimartingale BSDEs Under an Exponential Moments Condition. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) Séminaire de Probabilités XLIV. Lecture Notes in Mathematics(), vol 2046. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27461-9_5

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