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Improving the Asmussen–Kroese-Type Simulation Estimators

Part of: Probabilistic methods, simulation and stochastic differential equations Mathematical finance

Published online by Cambridge University Press:  30 January 2018

Samim Ghamami  and
Sheldon M. Ross
Samim Ghamami*
Affiliation:
University of Southern California
Sheldon M. Ross*
Affiliation:
University of Southern California
*
∗ Postal address: Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA 90089, USA.
∗ Postal address: Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA 90089, USA.
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Abstract

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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)+].

Keywords

Heavy-tailed random variablerare eventefficient Monte Carlo estimationvariance reductionconditioning; stratificationcontrol variatestop-loss transform

MSC classification

Primary: 65C05: Monte Carlo methods
Secondary: 91G20: Derivative securities
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 4 , December 2012 , pp. 1188 - 1193
Copyright
© 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.

References

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Ross, S. M. (2006). Simulation, 4th edn. Academic Press, San Diego, CA.Google Scholar