The transform likelihood ratio method for rare event simulation with heavy tails


Autoria(s): Kroese, D. P.; Rubinstein, R. Y.
Contribuinte(s)

E. Morozov

R. Serfozo

Data(s)

01/01/2004

Resumo

We present a novel method, called the transform likelihood ratio (TLR) method, for estimation of rare event probabilities with heavy-tailed distributions. Via a simple transformation ( change of variables) technique the TLR method reduces the original rare event probability estimation with heavy tail distributions to an equivalent one with light tail distributions. Once this transformation has been established we estimate the rare event probability via importance sampling, using the classical exponential change of measure or the standard likelihood ratio change of measure. In the latter case the importance sampling distribution is chosen from the same parametric family as the transformed distribution. We estimate the optimal parameter vector of the importance sampling distribution using the cross-entropy method. We prove the polynomial complexity of the TLR method for certain heavy-tailed models and demonstrate numerically its high efficiency for various heavy-tailed models previously thought to be intractable. We also show that the TLR method can be viewed as a universal tool in the sense that not only it provides a unified view for heavy-tailed simulation but also can be efficiently used in simulation with light-tailed distributions. We present extensive simulation results which support the efficiency of the TLR method.

Identificador

http://espace.library.uq.edu.au/view/UQ:68124/dpk_ryr_04_post_print.pdf

http://espace.library.uq.edu.au/view/UQ:68124

Idioma(s)

eng

Publicador

Springer New York LLC

Palavras-Chave #Computer Science, Interdisciplinary Applications #Operations Research & Management Science #Cross-entropy #Heavy Tail Distributions #Rare Events #Simulation #Importance Sampling #Likelihood Ratio #Monte-carlo #230202 Stochastic Analysis and Modelling #780101 Mathematical sciences #010405 Statistical Theory #010206 Operations Research
Tipo

Journal Article