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Numerical approximation of BSDEs using local polynomial drivers and branching processes

Author

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  • Bouchard Bruno

    (Université Paris-Dauphine, PSL Research University, CNRS, UMR [7534], Ceremade, 75016Paris, France)

  • Tan Xiaolu

    (Université Paris-Dauphine, PSL Research University, CNRS, UMR [7534], Ceremade, 75016Paris, France)

  • Warin Xavier

    (EDF/R&D, Laboratoire de Finance des Marchés de l’Energie, 92141ClamartCede, France)

  • Zou Yiyi

    (Université Paris-Dauphine, PSL Research University, CNRS, UMR [7534], Ceremade, 75016Paris, France)

Abstract

We propose a new numerical scheme for Backward Stochastic Differential Equations (BSDEs) based on branching processes. We approximate an arbitrary (Lipschitz) driver by local polynomials and then use a Picard iteration scheme. Each step of the Picard iteration can be solved by using a representation in terms of branching diffusion systems, thus avoiding the need for a fine time discretization. In contrast to the previous literature on the numerical resolution of BSDEs based on branching processes, we prove the convergence of our numerical scheme without limitation on the time horizon. Numerical simulations are provided to illustrate the performance of the algorithm.

Suggested Citation

  • Bouchard Bruno & Tan Xiaolu & Warin Xavier & Zou Yiyi, 2017. "Numerical approximation of BSDEs using local polynomial drivers and branching processes," Monte Carlo Methods and Applications, De Gruyter, vol. 23(4), pages 241-263, December.
    • Handle: RePEc:bpj:mcmeap:v:23:y:2017:i:4:p:241-263:n:3
    DOI: 10.1515/mcma-2017-0116
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    References listed on IDEAS

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    1. repec:dau:papers:123456789/4273 is not listed on IDEAS
    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. 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.
    4. Rasulov, A. & Raimova, G. & Mascagni, M., 2010. "Monte Carlo solution of Cauchy problem for a nonlinear parabolic equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(6), pages 1118-1123.
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    Cited by:

    1. Bruno Bouchard & Ki Wai Chau & Arij Manai & Ahmed Sid-Ali, 2019. "Monte-Carlo methods for the pricing of American options: a semilinear BSDE point of view," Post-Print hal-01666399, HAL.

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