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A parallel algorithm for solving BSDEs

Author

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  • Labart Céline

    (Laboratoire de Mathématiques, CNRS UMR 5127, Université de Savoie, Campus Scientifique, 73376 Le Bourget du Lac, France; and Projet MathRisk, INRIA Paris–Rocquencourt, France)

  • Lelong Jérôme

    (Université Grenoble Alpes, Laboratoire Jean Kuntzmann, 51, rue des Mathématiques, BP 53, 38041 Grenoble, Cedex 09, France; and Projet MathRisk, INRIA Paris–Rocquencourt, France)

Abstract

We present a parallel algorithm for solving backward stochastic differential equations. We improve the algorithm proposed by Gobet and Labart (2010) based on an adaptive Monte Carlo method with Picard's iterations, and propose a parallel version of it. We test our algorithm on linear and nonlinear drivers up to dimension 8 on a cluster of 312 CPUs. We obtained very encouraging efficiency ratios greater than 0.7.

Suggested Citation

  • Labart Céline & Lelong Jérôme, 2013. "A parallel algorithm for solving BSDEs," Monte Carlo Methods and Applications, De Gruyter, vol. 19(1), pages 11-39, March.
    • Handle: RePEc:bpj:mcmeap:v:19:y:2013:i:1:p:11-39:n:2
    DOI: 10.1515/mcma-2013-0001
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    References listed on IDEAS

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    1. Pierre L'Ecuyer & Richard Simard & E. Jack Chen & W. David Kelton, 2002. "An Object-Oriented Random-Number Package with Many Long Streams and Substreams," Operations Research, INFORMS, vol. 50(6), pages 1073-1075, December.
    2. Bouchard, Bruno & Touzi, Nizar, 2004. "Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 111(2), pages 175-206, June.
    3. Bally, Vlad & Pagès, Gilles, 2003. "Error analysis of the optimal quantization algorithm for obstacle problems," Stochastic Processes and their Applications, Elsevier, vol. 106(1), pages 1-40, July.
    4. Bender, Christian & Denk, Robert, 2007. "A forward scheme for backward SDEs," Stochastic Processes and their Applications, Elsevier, vol. 117(12), pages 1793-1812, December.
    5. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
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