Improving the Asmussen-Kroese-Type Simulation Estimators

Posted: 27 Oct 2013

See all articles by Samim Ghamami

Samim Ghamami

Securities and Exchange Commission (SEC); New York University (NYU); University of California, Berkeley - Center for Risk Management Research

Sheldon Ross

University of Southern California - Viterbi School of Engineering

Date Written: May 28, 2012

Abstract

The Asmussen-Kroese Monte Carlo estimators of P(S_n > u) and P(S_N > u) are known to work well in rare event settings, where S_N is the sum of independent, identically distributed heavy-tailed random variables X_1,...,X_N and N is a non-negative, integer-valued random variable independent of the X_i. In this paper we show how to improve the Asmussen-Kroese estimators of both probabilities when the X_i are non-negative. We also apply our ideas to estimate the quantity E[(S_N-u) ].

Keywords: Heavy-tailed random variables, efficient Monte Carlo simulation, Asmussen-Kroese estimators, stop-loss transform

JEL Classification: C15

Suggested Citation

Ghamami, Samim and Ross, Sheldon, Improving the Asmussen-Kroese-Type Simulation Estimators (May 28, 2012). Journal of Applied Probability, Vol. 49, No. 4, 2012, Available at SSRN: https://ssrn.com/abstract=2345764

Samim Ghamami (Contact Author)

Securities and Exchange Commission (SEC) ( email )

450 Fifth Street, NW
Washington, DC 20549-1105
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New York University (NYU) ( email )

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University of California, Berkeley - Center for Risk Management Research ( email )

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Sheldon Ross

University of Southern California - Viterbi School of Engineering ( email )

3650 McClintock Ave
Los Angeles, CA
United States

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