How many inner simulations to compute conditional expectations with least-square Monte Carlo?

Aurélien Alfonsi (), Bernard Lapeyre () and Jérôme Lelong ()
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Aurélien Alfonsi: MATHRISK - Mathematical Risk Handling - UPEM - Université Paris-Est Marne-la-Vallée - ENPC - École nationale des ponts et chaussées - Centre Inria de Paris - Inria - Institut National de Recherche en Informatique et en Automatique, CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École nationale des ponts et chaussées
Bernard Lapeyre: MATHRISK - Mathematical Risk Handling - UPEM - Université Paris-Est Marne-la-Vallée - ENPC - École nationale des ponts et chaussées - Centre Inria de Paris - Inria - Institut National de Recherche en Informatique et en Automatique, CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École nationale des ponts et chaussées
Jérôme Lelong: DAO - Données, Apprentissage et Optimisation - LJK - Laboratoire Jean Kuntzmann - Inria - Institut National de Recherche en Informatique et en Automatique - CNRS - Centre National de la Recherche Scientifique - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes

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Abstract: The problem of computing the conditional expectation E[f (Y)|X] with least-square Monte-Carlo is of general importance and has been widely studied. To solve this problem, it is usually assumed that one has as many samples of Y as of X. However, when samples are generated by computer simulation and the conditional law of Y given X can be simulated, it may be relevant to sample K ∈ N values of Y for each sample of X. The present work determines the optimal value of K for a given computational budget, as well as a way to estimate it. The main take away message is that the computational gain can be all the more important that the computational cost of sampling Y given X is small with respect to the computational cost of sampling X. Numerical illustrations on the optimal choice of K and on the computational gain are given on different examples including one inspired by risk management.

Keywords: Least square Monte-Carlo; Conditional expectation estimators; Variance reduction (search for similar items in EconPapers)
Date: 2023-06-20
New Economics Papers: this item is included in nep-cmp and nep-ecm
Note: View the original document on HAL open archive server: https://hal.science/hal-03770051v2
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Published in Methodology and Computing in Applied Probability, 2023, 25 (3), pp.71. ⟨10.1007/s11009-023-10038-x⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03770051

DOI: 10.1007/s11009-023-10038-x

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