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On the Robustness of the Snell envelope

hal.structure.identifierAdvanced Learning Evolutionary Algorithms [ALEA]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorDEL MORAL, Pierre
hal.structure.identifierAdvanced Learning Evolutionary Algorithms [ALEA]
dc.contributor.authorHU, P.
hal.structure.identifierLaboratoire Analyse, Géométrie et Applications [LAGA]
hal.structure.identifierEDF [EDF]
dc.contributor.authorOUDJANE, Nadia
hal.structure.identifierMéthodes Quantitatives de Gestion [MQG]
dc.contributor.authorRÉMILLARD, Bruno
dc.date.issued2011
dc.description.abstractEnWe analyze the robustness properties of the Snell envelope backward evolution equation for the discrete time optimal stopping problem. We consider a series of approximation schemes, including cut-off type approximations, Euler discretization schemes, interpolation models, quantization tree models, and the Stochastic Mesh method of Broadie-Glasserman. In each situation, we provide non asymptotic convergence estimates, including Lp-mean error bounds and exponential concentration inequalities. We deduce these estimates from a single and general robustness property of Snell envelope semigroups. In particular, this analysis allows us to recover existing convergence results for the quantization tree method and to improve significantly the rates of convergence obtained for the Stochastic Mesh estimator of Broadie-Glasserman. In the second part of the article, we propose a new approach using a genealogical tree approximation of the reference Markov process in terms of a neutral type genetic model. In contrast to Broadie-Glasserman Monte Carlo models, the computational cost of this new stochastic particle approximation is linear in the number of sampled points. Some simulations results are provided and confirm the interest of this new algorithm.
dc.language.isoen
dc.publisherSociety for Industrial and Applied Mathematics
dc.subject.enSnell envelope
dc.subject.enoptimal stopping
dc.subject.enAmerican option pricing
dc.subject.engenealogical trees
dc.subject.eninteracting particle model
dc.title.enOn the Robustness of the Snell envelope
dc.typeArticle de revue
dc.identifier.doi10.1137/100798016
dc.subject.halStatistiques [stat]/Applications [stat.AP]
bordeaux.journalSIAM Journal on Financial Mathematics
bordeaux.page951-997
bordeaux.volume2
bordeaux.peerReviewedoui
hal.identifierhal-00641452
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00641452v1
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