A nonintrusive stratified resampler for regression monte carlo: Application to solving nonlinear equations

Emmanuel Gobet; L. I.U. Gang; Jorge P. Zubelli

doi:10.1137/16M1066865

A nonintrusive stratified resampler for regression monte carlo: Application to solving nonlinear equations

Emmanuel Gobet, L. I.U. Gang, Jorge P. Zubelli

Mathematics

Université Paris 11

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Our goal is to solve certain dynamic programming equations associated to a given Markov chain X, using a regression-based Monte Carlo algorithm. More specifically, we assume that the model for X is not known in full detail and only a root sample X¹, . . ., X^M of such process is available. By a stratification of the space and a suitable choice of a probability measure ν, we design a new resampling scheme that allows us to compute local regressions (on basis functions) in each stratum. The combination of the stratification and the resampling allows us to compute the solution to the dynamic programming equation (possibly in large dimensions) using only a relatively small set of root paths. To assess the accuracy of the algorithm, we establish nonasymptotic error estimates in L²(ν). Our numerical experiments illustrate the good performance, even with M = 20 − 40 root paths.

Original language	British English
Pages (from-to)	50-77
Number of pages	28
Journal	SIAM Journal on Numerical Analysis
Volume	56
Issue number	1
DOIs	https://doi.org/10.1137/16M1066865
State	Published - 2018

Keywords

Discrete dynamic programming equations
Empirical regression scheme
Resampling methods
Small-size sample

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10.1137/16M1066865

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title = "A nonintrusive stratified resampler for regression monte carlo: Application to solving nonlinear equations",

abstract = "Our goal is to solve certain dynamic programming equations associated to a given Markov chain X, using a regression-based Monte Carlo algorithm. More specifically, we assume that the model for X is not known in full detail and only a root sample X1, . . ., XM of such process is available. By a stratification of the space and a suitable choice of a probability measure ν, we design a new resampling scheme that allows us to compute local regressions (on basis functions) in each stratum. The combination of the stratification and the resampling allows us to compute the solution to the dynamic programming equation (possibly in large dimensions) using only a relatively small set of root paths. To assess the accuracy of the algorithm, we establish nonasymptotic error estimates in L2(ν). Our numerical experiments illustrate the good performance, even with M = 20 − 40 root paths.",

keywords = "Discrete dynamic programming equations, Empirical regression scheme, Resampling methods, Small-size sample",

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AU - Gang, L. I.U.

AU - Zubelli, Jorge P.

PY - 2018

Y1 - 2018

N2 - Our goal is to solve certain dynamic programming equations associated to a given Markov chain X, using a regression-based Monte Carlo algorithm. More specifically, we assume that the model for X is not known in full detail and only a root sample X1, . . ., XM of such process is available. By a stratification of the space and a suitable choice of a probability measure ν, we design a new resampling scheme that allows us to compute local regressions (on basis functions) in each stratum. The combination of the stratification and the resampling allows us to compute the solution to the dynamic programming equation (possibly in large dimensions) using only a relatively small set of root paths. To assess the accuracy of the algorithm, we establish nonasymptotic error estimates in L2(ν). Our numerical experiments illustrate the good performance, even with M = 20 − 40 root paths.

AB - Our goal is to solve certain dynamic programming equations associated to a given Markov chain X, using a regression-based Monte Carlo algorithm. More specifically, we assume that the model for X is not known in full detail and only a root sample X1, . . ., XM of such process is available. By a stratification of the space and a suitable choice of a probability measure ν, we design a new resampling scheme that allows us to compute local regressions (on basis functions) in each stratum. The combination of the stratification and the resampling allows us to compute the solution to the dynamic programming equation (possibly in large dimensions) using only a relatively small set of root paths. To assess the accuracy of the algorithm, we establish nonasymptotic error estimates in L2(ν). Our numerical experiments illustrate the good performance, even with M = 20 − 40 root paths.

KW - Discrete dynamic programming equations

KW - Empirical regression scheme

KW - Resampling methods

KW - Small-size sample

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A nonintrusive stratified resampler for regression monte carlo: Application to solving nonlinear equations

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