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December 2012 Improving the Asmusse}--Kroese-type simulation estimators
Samim Ghamami, Sheldon M. Ross
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J. Appl. Probab. 49(4): 1188-1193 (December 2012). DOI: 10.1239/jap/1354716666

Abstract

The Asmussen--Kroese Monte Carlo estimators of P(Sn > u) and P(SN > u) are known to work well in rare event settings, where SN is the sum of independent, identically distributed heavy-tailed random variables X1,...,XN and N is a nonnegative, integer-valued random variable independent of the Xi. In this paper we show how to improve the Asmussen--Kroese estimators of both probabilities when the Xi are nonnegative. We also apply our ideas to estimate the quantity E[(SN-u)+].

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Samim Ghamami. Sheldon M. Ross. "Improving the Asmusse}--Kroese-type simulation estimators." J. Appl. Probab. 49 (4) 1188 - 1193, December 2012. https://doi.org/10.1239/jap/1354716666

Information

Published: December 2012
First available in Project Euclid: 5 December 2012

zbMATH: 1255.91426
MathSciNet: MR3058997
Digital Object Identifier: 10.1239/jap/1354716666

Subjects:
Primary: 65C05
Secondary: 91G20

Keywords: conditioning; stratification , control variate , efficient Monte Carlo estimation , Heavy-tailed random variable , Rare event , stop-loss transform , variance reduction

Rights: Copyright © 2012 Applied Probability Trust

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Vol.49 • No. 4 • December 2012
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