Show simple item record

dc.contributor.authorHoel, Hakon
dc.contributor.authorVon Schwerin, Erik
dc.contributor.authorSzepessy, Anders
dc.contributor.authorTempone, Raul
dc.date.accessioned2015-08-03T11:45:44Z
dc.date.available2015-08-03T11:45:44Z
dc.date.issued2014-01-01
dc.identifier.issn09299629
dc.identifier.doi10.1515/mcma-2013-0014
dc.identifier.urihttp://hdl.handle.net/10754/563323
dc.description.abstractWe present an adaptive multilevel Monte Carlo (MLMC) method for weak approximations of solutions to Itô stochastic dierential equations (SDE). The work [11] proposed and analyzed an MLMC method based on a hierarchy of uniform time discretizations and control variates to reduce the computational effort required by a single level Euler-Maruyama Monte Carlo method from O(TOL-3) to O(TOL-2 log(TOL-1)2) for a mean square error of O(TOL2). Later, the work [17] presented an MLMC method using a hierarchy of adaptively re ned, non-uniform time discretizations, and, as such, it may be considered a generalization of the uniform time discretizationMLMC method. This work improves the adaptiveMLMC algorithms presented in [17] and it also provides mathematical analysis of the improved algorithms. In particular, we show that under some assumptions our adaptive MLMC algorithms are asymptotically accurate and essentially have the correct complexity but with improved control of the complexity constant factor in the asymptotic analysis. Numerical tests include one case with singular drift and one with stopped diusion, where the complexity of a uniform single level method is O(TOL-4). For both these cases the results con rm the theory, exhibiting savings in the computational cost for achieving the accuracy O(TOL) from O(TOL-3) for the adaptive single level algorithm to essentially O(TOL-2 log(TOL-1)2) for the adaptive MLMC algorithm. © 2014 by Walter de Gruyter Berlin/Boston 2014.
dc.publisherWalter de Gruyter GmbH
dc.subjecta posteriori error estimates
dc.subjectadaptivity
dc.subjectadjoints
dc.subjectbackward dual functions
dc.subjectComputational finance
dc.subjecterror control
dc.subjectEuler-Maruyama method
dc.subjectMonte Carlo
dc.subjectmultilevel
dc.subjectweak approximation
dc.titleImplementation and analysis of an adaptive multilevel Monte Carlo algorithm
dc.typeArticle
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentStochastic Numerics Research Group
dc.identifier.journalMonte Carlo Methods and Applications
dc.contributor.institutionCSQI-MATHICSE, École Polytechnique Fédérale de Lausanne, Switzerland
dc.contributor.institutionDepartment of Mathematics, Royal Institute of Technology (KTH), Stockholm, Sweden
kaust.personHoel, Hakon
kaust.personTempone, Raul


This item appears in the following Collection(s)

Show simple item record