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Bounded Relative Error Importance Sampling and Rare Event Simulation

Published online by Cambridge University Press:  09 August 2013

Don L. McLeish
Don L. McLeish*
Affiliation:
Department of Statistics and Actuarial Science, University of Waterloo, Canada
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Abstract

We consider estimating tail events using exponential families of importance sampling distributions. When the cannonical sufficient statistic for the exponential family mimics the tail behaviour of the underlying cumulative distribution function, we can achieve bounded relative error for estimating tail probabilities. Examples of rare event simulation from various distributions including Tukey's g&h distribution are provided.

Keywords

Rare event simulationrelative errorg&h distributionMonte Carlo methodsImportance samplingCross-entropyRényi Divergence
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 40 , Issue 1 , May 2010 , pp. 377 - 398
Copyright
Copyright © International Actuarial Association 2010

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References

Asmussen, S. and Glynn, P.W. (2007) Stochastic simulation: algorithms and analysis, Springer, New York.Google Scholar
Asmussen, S., Kroese, D.P. and Rubinstein, R.Y. (2005) Heavy tails, importance sampling and cross-entropy. Stochastic Models, 21, 57–76.Google Scholar
Bingham, N.H., Goldie, C.M. and Teugels, J.L. (1987) Regular Variation, Encyclopedia of Mathematics and its Applications, Cambridge University Press.CrossRefGoogle Scholar
Dupuis, D.J. and Field, C.A. (2004) Large wind speeds: modeling and outlier detection, J. Agricultural Biol. Environ. Statist., 9, 105–121.Google Scholar
Dutta, K. and Perry, J. (2006) A tale of tails: an empirical analysis of loss distribution models for estimating operational riskcapital. Federal Reserve Bank of Boston, Working Paper N° 06–13.Google Scholar
Degen, M., Embrechts, P. and Lambrigger, D.D. (2007) The quantitative modeling of operational risk: between g-and-h and EVT. ASTIN Bulletin 37(2), 265–291.Google Scholar
Field, C. and Genton, M.G. (2006) The multivariate g-and-h distribution Technometrics, 48, 104–111.Google Scholar
Homem-De-Mello, T. and Rubinstein, R.Y. (2002) Rare event simulation and combinatorial optimization using cross entropy: estimation of rare event probabilities using cross-entropy Proceedings of the 34th Conference on Winter Simulation: exploring new frontiers, 310–319.Google Scholar
Kroese, D. and Rubinstein, R.Y. (2008) Simulationand the Monte Carlo Method. (Second Edition) Wiley, New York.Google Scholar
McLeish, D.L. (2005) Monte Carlo Simulation and Finance. Wiley, New York.Google Scholar
McNeil, A.J., Frey, R. and Embrechts, P. (2005) Quantitative Risk Management, Princeton University Press, Princeton.Google Scholar
Mikosch, T. (1999) Regular Variation, Subexponentiality and Their Applications in Probability Theory. EURANDOM Report 99–013.Google Scholar
Rényi, A. (1961) On Measures of entropy and information. Proceedings of the 4th Berkeley symposium on mathematical statistics and probability. Editor, Neyman, , University of California Press, Berkeley, Calif. 547–561.Google Scholar
Ridder, A. and Rubinstein, R. (2007) Minimum cross-entropy methods for rareevent simulation. Simulation, 83,769–784.CrossRefGoogle Scholar