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Rare-event simulation for a multidimensional random walk with t distributed increments

Published: 09 December 2007 Publication History

Abstract

We consider the problem of efficient estimation of first passage time probabilities for a multidimensional random walk with t distributed increments, via simulation. In addition of being a natural generalization of the problem of computing ruin probabilities in insurance -- in which the focus is a one dimensional random walk -- this problem captures important features of large deviations for multidimensional heavy-tailed processes (such as the role played by the mean of the random walk in connection to the spatial location of the target set). We develop a state-dependent importance sampling estimator for this class of multidimensional problems. Then, we argue -- using techniques based on Lyapunov type inequalities -- that our estimator is strongly efficient.

References

[1]
Asmussen, S. (2003) Applied Probability and Queues. Springer-Verlag. New York.
[2]
Blanchet, J. and Glynn, P. (2007) Efficient rare event simulation for the maximum of heavy-tailed random walks. Submitted.
[3]
Blanchet, J., Glynn, P., and Liu, J. C. (2007a) Fluid heuristics, Lyapunov bounds and efficient importance sampling for a heavy-tailed G/G/1 queue. Submitted.
[4]
Blanchet, J., Glynn, P., and Liu, J. C. (2007b) Efficient rare event simulation for multiserver queues. Preprint.
[5]
Blanchet, J. and Liu, J. C. (2007) First-passage time probabilities for multidimensional heavy-tailed random walks: Algorithms and Asymptotics. Preprint.
[6]
Dupuis, P., Leder, K., and Wang, H. (2006) Notes on importance sampling for random variables with regularly varying tails. Preprint.
[7]
Embrechts, P., Lindskog, F., and McNeal, A. (2001) Modeling dependence with copulas and applications to risk management. Technical Report, Risklab, ETH Zurich.
[8]
Glasserman, P., and Juneja, S. (2007) Uniformly Efficient Importance Sampling for the Tail Distribution of Sums of Random Variables. To appear in Math. of O.R.
[9]
Glynn, P., and Iglehart, D. (1989) Importance sampling for stochastic simulations. Management Science, vol.35, No.11, p.1367--1392.
[10]
Hult, H., Lindskog, F., Mikosch, T., and Samorodnitsky, G. (2005) Functional large deviations for multivariate regularly varying random walks. Ann. Appl. Probab. No. 15, p. 2651--2680.
[11]
Hult, H., and Lindskog, F. (2006) Heavy-tailed insurance portfolios: buffer capital and ruin probabilities. Tech. Rep. No. 1441, School of ORIE, Cornell University.
[12]
Rozovskii, L. V. (1989) Probabilities of Large Deviations of Sums of Independent Random Variables with Common Distribution Function in the Domain of Attraction of the Normal Law, Theory Probab. Appl., 34, pp. 625--644.
[13]
Sadowsky, J. S. and Bucklew, J. A. (1990) On large deviations theory and asymptotically efficient Monte Carlo estimation. IEEE Transactions on Information Theory, Vol. 36, No 3, p. 579--588.

Cited By

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  • (2009)Introduction of first passage time (FPT) analysis for software reliability and network securityProceedings of the 5th Annual Workshop on Cyber Security and Information Intelligence Research: Cyber Security and Information Intelligence Challenges and Strategies10.1145/1558607.1558680(1-6)Online publication date: 13-Apr-2009

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Published In

cover image ACM Conferences
WSC '07: Proceedings of the 39th conference on Winter simulation: 40 years! The best is yet to come
December 2007
2659 pages
ISBN:1424413060

Sponsors

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

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IEEE Press

Publication History

Published: 09 December 2007

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  • Research-article

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WSC07
Sponsor:
  • IIE
  • INFORMS-SIM
  • ASA
  • IEEE/SMC
  • SIGSIM
  • NIST
  • (SCS)
WSC07: Winter Simulation Conference
December 9 - 12, 2007
Washington D.C.

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WSC '07 Paper Acceptance Rate 152 of 244 submissions, 62%;
Overall Acceptance Rate 3,413 of 5,075 submissions, 67%

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Cited By

View all
  • (2009)Introduction of first passage time (FPT) analysis for software reliability and network securityProceedings of the 5th Annual Workshop on Cyber Security and Information Intelligence Research: Cyber Security and Information Intelligence Challenges and Strategies10.1145/1558607.1558680(1-6)Online publication date: 13-Apr-2009

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