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Improving the Asmussen–Kroese-Type Simulation Estimators
Published online by Cambridge University Press: 30 January 2018
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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- Research Article
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- © Applied Probability Trust
Footnotes
Accepted by Onno Boxma, Coordinating Editor.
This material is based upon work supported by the US Army Research Laboratory and the US Army Research Office under grant number W911NF-11-1-0115.
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