Article

Applied Mathematics & Optimization

, Volume 66, Issue 3, pp 309-330

Snell Envelope with Small Probability Criteria

  • Pierre Del MoralAffiliated withCentre INRIA Bordeaux et Sud-Ouest & Institut de Mathématiques de Bordeaux, Université de Bordeaux I
  • , Peng HuAffiliated withCentre INRIA Bordeaux et Sud-Ouest & Institut de Mathématiques de Bordeaux, Université de Bordeaux I Email author 
  • , Nadia OudjaneAffiliated withEDF R&D ClamartUniversité 13 and FiME (Laboratoire de Finance des Marchés de l’Energie (Dauphine, CREST, EDF R&D))

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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.

Keywords

Snell envelope American option Bermudan option Stochastic mesh Particle methods Rare events