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September 2013 Efficient simulation of large deviation events for sums of random vectors using saddle-point representations
Ankush Agarwal, Santanu Dey, Sandeep Juneja
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J. Appl. Probab. 50(3): 703-720 (September 2013). DOI: 10.1239/jap/1378401231

Abstract

We consider the problem of efficient simulation estimation of the density function at the tails, and the probability of large deviations for a sum of independent, identically distributed (i.i.d.), light-tailed, and nonlattice random vectors. The latter problem besides being of independent interest, also forms a building block for more complex rare event problems that arise, for instance, in queueing and financial credit risk modeling. It has been extensively studied in the literature where state-independent, exponential-twisting-based importance sampling has been shown to be asymptotically efficient and a more nuanced state-dependent exponential twisting has been shown to have a stronger bounded relative error property. We exploit the saddle-point-based representations that exist for these rare quantities, which rely on inverting the characteristic functions of the underlying random vectors. These representations reduce the rare event estimation problem to evaluating certain integrals, which may via importance sampling be represented as expectations. Furthermore, it is easy to identify and approximate the zero-variance importance sampling distribution to estimate these integrals. We identify such importance sampling measures and show that they possess the asymptotically vanishing relative error property that is stronger than the bounded relative error property. To illustrate the broader applicability of the proposed methodology, we extend it to develop an asymptotically vanishing relative error estimator for the practically important expected overshoot of sums of i.i.d. random variables.

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Ankush Agarwal. Santanu Dey. Sandeep Juneja. "Efficient simulation of large deviation events for sums of random vectors using saddle-point representations." J. Appl. Probab. 50 (3) 703 - 720, September 2013. https://doi.org/10.1239/jap/1378401231

Information

Published: September 2013
First available in Project Euclid: 5 September 2013

zbMATH: 1282.65025
MathSciNet: MR3102510
Digital Object Identifier: 10.1239/jap/1378401231

Subjects:
Primary: 60E10, 60F10, 65C05
Secondary: 65C50, 65T99

Rights: Copyright © 2013 Applied Probability Trust

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Vol.50 • No. 3 • September 2013
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