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Snell Envelope with Small Probability Criteria

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Abstract

We present a new algorithm to compute the Snell envelope in the specific case where the criteria to optimize is associated with a small probability or a rare event. This new approach combines the Stochastic Mesh approach of Broadie and Glasserman with a particle approximation scheme based on a specific change of measure designed to concentrate the computational effort in regions pointed out by the criteria. The theoretical analysis of this new algorithm provides non asymptotic convergence estimates. Finally, the numerical tests confirm the practical interest of this approach.

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Authors and Affiliations

  1. Centre INRIA Bordeaux et Sud-Ouest & Institut de Mathématiques de Bordeaux, Université de Bordeaux I, 351 cours de la Libération, 33405, Talence cedex, France

    Pierre Del Moral & Peng Hu

  2. EDF R&D Clamart, Clamart, France

    Nadia Oudjane

  3. Université 13 and FiME (Laboratoire de Finance des Marchés de l’Energie (Dauphine, CREST, EDF R&D)), Paris, France

    Nadia Oudjane

Authors
  1. Pierre Del Moral
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  2. Peng Hu
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  3. Nadia Oudjane
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Correspondence to Peng Hu.

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Del Moral, P., Hu, P. & Oudjane, N. Snell Envelope with Small Probability Criteria. Appl Math Optim 66, 309–330 (2012). https://doi.org/10.1007/s00245-012-9173-1

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  • DOI: https://doi.org/10.1007/s00245-012-9173-1

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