On the inefficiency of state-independent importance sampling in the presence of heavy tails

Authors:
Achal Bassamboo;Sandeep Juneja;Assaf Zeevi
Affiliations:
Northwestern University, Kellogg School of Management, USA;Tata Institute of Fundamental Research, School of Technology and Computer Science, India;Columbia University, Graduate School of Business, USA
Venue:
Operations Research Letters
Year:
2007

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Abstract

This paper proves that there does not exist an asymptotically optimal state-independent change-of-measure for estimating the probability that a random walk with heavy-tailed increments exceeds a ''high'' threshold before going below zero. Explicit bounds are given on the best asymptotic variance reduction that can be achieved by state-independent schemes.