On Monte Carlo and Quasi-Monte Carlo Methods for Series Representation of Infinitely Divisible Laws

Reiichiro Kawai, Junichi Imai

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

Infinitely divisible random vectors and Lévy processes without Gaussian component admit representations with shot noise series. To enhance efficiency of the series representation in Monte Carlo simulations, we discuss variance reduction methods, such as stratified sampling, control variates and importance sampling, applied to exponential interarrival times forming the shot noise series. We also investigate the applicability of the generalized linear transformation method in the quasi-Monte Carlo framework to random elements of the series representation. Although implementation of the proposed techniques requires a small amount of initial work, the techniques have the potential to yield substantial improvements in estimator efficiency, as the plain use of the series representation in those frameworks is often expensive. Numerical results are provided to illustrate the effectiveness of our approaches.

Original languageEnglish
Title of host publicationSpringer Proceedings in Mathematics and Statistics
PublisherSpringer New York LLC
Pages471-486
Number of pages16
Volume23
ISBN (Print)9783642274398
DOIs
Publication statusPublished - 2012
Event9th International Conference on Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing, MCQMC 2010 - Warsaw, Poland
Duration: 2010 Aug 152010 Aug 20

Other

Other9th International Conference on Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing, MCQMC 2010
CountryPoland
CityWarsaw
Period10/8/1510/8/20

Fingerprint

Infinitely Divisible Laws
Quasi-Monte Carlo Methods
Series Representation
Shot Noise
Control Variates
Stratified Sampling
Quasi-Monte Carlo
Infinitely Divisible
Random Element
Variance Reduction
Series
Importance Sampling
Exponential time
Linear transformation
Random Vector
Reduction Method
Monte Carlo Simulation
Estimator
Numerical Results
Framework

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Kawai, R., & Imai, J. (2012). On Monte Carlo and Quasi-Monte Carlo Methods for Series Representation of Infinitely Divisible Laws. In Springer Proceedings in Mathematics and Statistics (Vol. 23, pp. 471-486). Springer New York LLC. https://doi.org/10.1007/978-3-642-27440-4_26

On Monte Carlo and Quasi-Monte Carlo Methods for Series Representation of Infinitely Divisible Laws. / Kawai, Reiichiro; Imai, Junichi.

Springer Proceedings in Mathematics and Statistics. Vol. 23 Springer New York LLC, 2012. p. 471-486.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Kawai, R & Imai, J 2012, On Monte Carlo and Quasi-Monte Carlo Methods for Series Representation of Infinitely Divisible Laws. in Springer Proceedings in Mathematics and Statistics. vol. 23, Springer New York LLC, pp. 471-486, 9th International Conference on Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing, MCQMC 2010, Warsaw, Poland, 10/8/15. https://doi.org/10.1007/978-3-642-27440-4_26
Kawai R, Imai J. On Monte Carlo and Quasi-Monte Carlo Methods for Series Representation of Infinitely Divisible Laws. In Springer Proceedings in Mathematics and Statistics. Vol. 23. Springer New York LLC. 2012. p. 471-486 https://doi.org/10.1007/978-3-642-27440-4_26
Kawai, Reiichiro ; Imai, Junichi. / On Monte Carlo and Quasi-Monte Carlo Methods for Series Representation of Infinitely Divisible Laws. Springer Proceedings in Mathematics and Statistics. Vol. 23 Springer New York LLC, 2012. pp. 471-486
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