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Monte-Carlo algorithms for a forward Feynman–Kac-type representation for semilinear nonconservative partial differential equations

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  • Le Cavil Anthony

    (ENSTA ParisTech, Université Paris-Saclay, Unité de Mathématiques Appliquées (UMA), 828 Bd. des Maréchaux, 91120 Palaiseau, France)

  • Oudjane Nadia

    (EDF Lab Paris-Saclay and FiME, Laboratoire de Finance des Marchés de l’Energie, 7 Boulevard Gaspard Monge, 91120 Palaiseau, France)

  • Russo Francesco

    (ENSTA ParisTech, Université Paris-Saclay, Unité de Mathématiques Appliquées (UMA), 828 Bd. des Maréchaux, 91120 Palaiseau, France)

Abstract

The paper is devoted to the construction of a probabilistic particle algorithm. This is related to a nonlinear forward Feynman–Kac-type equation, which represents the solution of a nonconservative semilinear parabolic partial differential equation (PDE). Illustrations of the efficiency of the algorithm are provided by numerical experiments.

Suggested Citation

  • Le Cavil Anthony & Oudjane Nadia & Russo Francesco, 2018. "Monte-Carlo algorithms for a forward Feynman–Kac-type representation for semilinear nonconservative partial differential equations," Monte Carlo Methods and Applications, De Gruyter, vol. 24(1), pages 55-70, March.
    • Handle: RePEc:bpj:mcmeap:v:24:y:2018:i:1:p:55-70:n:5
    DOI: 10.1515/mcma-2018-0005
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    References listed on IDEAS

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    1. 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.
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