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Multilevel Monte Carlo metamodeling

Published: 08 December 2013 Publication History

Abstract

Multilevel Monte Carlo (MLMC) methods have been used by the information-based complexity community in order to improve the computational efficiency of parametric integration. We extend this approach by relaxing the assumptions on differentiability of the simulation output. Relaxing the assumption on the differentiability of the simulation output makes the MLMC method more widely applicable to stochastic simulation metamodeling problems in industrial engineering. The proposed scheme uses a sequential experiment design which allocates effort unevenly among design points in order to increase its efficiency. The procedure's efficiency is tested on an example of option pricing in the Black-Scholes model.

References

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Ankenman, B. E., B. L. Nelson, and J. Staum. 2010. "Stochastic Kriging for Simulation Metamodeling". Operations Research 58 (2): 371--382.
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Barton, R. R. 1998. "Simulation metamodels". In Proceedings of the 30th conference on Winter simulation, WSC '98, 167--176. Los Alamitos, CA, USA: IEEE Computer Society Press.
[3]
Cliffe, K., M. Giles, R. Scheichl, and A. Teckentrup. 2011, January. "Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients". Computing and Visualization in Science 14 (1): 3--15.
[4]
Giles, M. B. 2008. "Multi-level Monte Carlo path simulation". Operations Research 56 (3): 607--617.
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Glasserman, P. 2003. Monte Carlo Methods in Financial Engineering (Stochastic Modelling and Applied Probability) (v. 53). 1 ed. Springer.
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Hastie, T., R. Tibshirani, and J. H. Friedman. 2003, July. The Elements of Statistical Learning. Corrected ed. Springer.
[7]
Heinrich, S. 2000. "The multilevel method of dependent tests". In Advances in Stochastic Simulation Methods, 47--62.
[8]
Kleijnen, J. P., and R. G. Sargent. 1997. "A Methodology for Fitting and Validating Metamodels in Simulation". European Journal of Operational Research 120:14--29.

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Information & Contributors

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Published In

cover image ACM Conferences
WSC '13: Proceedings of the 2013 Winter Simulation Conference: Simulation: Making Decisions in a Complex World
December 2013
4386 pages
ISBN:9781479920778

Sponsors

  • IIE: Institute of Industrial Engineers
  • INFORMS-SIM: Institute for Operations Research and the Management Sciences: Simulation Society
  • ASA: American Statistical Association
  • SIGSIM: ACM Special Interest Group on Simulation and Modeling
  • SCS: Society for Modeling and Simulation International
  • ASIM: Arbeitsgemeinschaft Simulation
  • IEEE/SMCS: Institute of Electrical and Electronics Engineers/Systems, Man, and Cybernetics Society
  • NIST: National Institute of Standards & Technology

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IEEE Press

Publication History

Published: 08 December 2013

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  • Research-article

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WSC '13
Sponsor:
  • IIE
  • INFORMS-SIM
  • ASA
  • SIGSIM
  • SCS
  • ASIM
  • IEEE/SMCS
  • NIST
WSC '13: Winter Simulation Conference
December 8 - 11, 2013
D.C., Washington

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Overall Acceptance Rate 3,413 of 5,075 submissions, 67%

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