Variance Reduction Techniques in Monte Carlo Methods

CentER Discussion Paper Series No. 2010-117

18 Pages Posted: 26 Nov 2010 Last revised: 5 Dec 2010

See all articles by Jack P. C. Kleijnen

Jack P. C. Kleijnen

Tilburg University, CentER

Ad Ridder

VU University Amsterdam - Department of Econometrics and Operations Research; Tinbergen Institute

Reuven Rubinstein

Technion-Israel Institute of Technology - The William Davidson Faculty of Industrial Engineering & Management

Date Written: November 2, 2010

Abstract

Monte Carlo methods are simulation algorithms to estimate a numerical quantity in a statistical model of a real system. These algorithms are executed by computer programs. Variance reduction techniques (VRT) are needed, even though computer speed has been increasing dramatically, ever since the introduction of computers. This increased computer power has stimulated simulation analysts to develop ever more realistic models, so that the net result has not been faster execution of simulation experiments; e.g., some modern simulation models need hours or days for a single ’run’ (one replication of one scenario or combination of simulation input values). Moreover there are some simulation models that represent rare events which have extremely small probabilities of occurrence), so even modern computer would take ’for ever’ (centuries) to execute a single run.were it not that special VRT can reduce theses excessively long runtimes to practical magnitudes.

Keywords: common random numbers, antithetic random numbers, importance sampling,control variates, conditioning, stratified sampling, splitting, quasi Monte Carlo

JEL Classification: C0, C1, C9

Suggested Citation

Kleijnen, Jack P.C. and Ridder, Ad and Rubinstein, Reuven, Variance Reduction Techniques in Monte Carlo Methods (November 2, 2010). CentER Discussion Paper Series No. 2010-117, Available at SSRN: https://ssrn.com/abstract=1715474 or http://dx.doi.org/10.2139/ssrn.1715474

Jack P.C. Kleijnen (Contact Author)

Tilburg University, CentER ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands
+31 13 4662029 (Phone)
+31 13 4663377 (Fax)

HOME PAGE: http://https://sites.google.com/site/kleijnenjackpc/

Ad Ridder

VU University Amsterdam - Department of Econometrics and Operations Research ( email )

De Boelelaan 1105
1081 HV Amsterdam
Netherlands

HOME PAGE: http://personal.vu.nl/a.a.n.ridder/

Tinbergen Institute ( email )

Gustav Mahlerplein 117
Amsterdam, 1082 MS
Netherlands

Reuven Rubinstein

Technion-Israel Institute of Technology - The William Davidson Faculty of Industrial Engineering & Management ( email )

Haifa 32000
Israel
972-4-8294458 (Phone)
972-4-8235194 (Fax)

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