Efficient Simulation for Large Deviation Probabilities of Heavy-tailed Sums (with J. C. Liu).

Summary:

This is the first paper that shows how to develop strongly efficient (i.e. bounded coefficient of variation) estimators for the simple problem of computing P(S_n > n*a) where S_n is the sum of $n$ i.i.d. mean zero, finite variance, regularly varying random variables. The light-tailed analogue (in the simulation context) can be traced back to the work of Siegmund in the 70’s and Sadowsky in the 90’s. The technique that we use takes advantage of Lyapunov inequalities. A related paper is “State-dependent Importance Sampling for Regularly Varying Random Walks”, in which we provide completely different algorithm (slightly more efficient because it avoids the need for computing a normalizing constant) and we also consider problems with more than one jump.

Bibtex:

@inproceedings{BL06,

author = {Blanchet, Jose H. and Liu, Jingchen},

title = {Efficient simulation for large deviation probabilities of sums of heavy-tailed increments},

booktitle = {Proceedings of the 38th Winter Simulation Conference},

series = {WSC '06},

year = {2006},

isbn = {1-4244-0501-7},

location = {Monterey, California},

pages = {757--764},

numpages = {8},

url = {http://portal.acm.org/citation.cfm?id=1218112.1218253},

acmid = {1218253},

publisher = {Winter Simulation Conference},

}