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Moderate deviation principles for importance sampling estimators of risk measures

Part of: Parametric inference Limit theorems Probabilistic methods, simulation and stochastic differential equations Applications

Published online by Cambridge University Press:  22 June 2017

Pierre Nyquist
Pierre Nyquist*
Affiliation:
Brown University
*
* Current address: Department of Mathematics, KTH Royal Institute of Technology, 100 44, Stockholm, Sweden. Email address: pierren@kth.se
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Abstract

Importance sampling has become an important tool for the computation of extreme quantiles and tail-based risk measures. For estimation of such nonlinear functionals of the underlying distribution, the standard efficiency analysis is not necessarily applicable. In this paper we therefore study importance sampling algorithms by considering moderate deviations of the associated weighted empirical processes. Using a delta method for large deviations, combined with classical large deviation techniques, the moderate deviation principle is obtained for importance sampling estimators of two of the most common risk measures: value at risk and expected shortfall.

Keywords

Large deviationmoderate deviationrisk measureempirical processasymptoticsimportance samplingMonte Carlo

MSC classification

Primary: 60F10: Large deviations 65C05: Monte Carlo methods
Secondary: 62F12: Asymptotic properties of estimators 62P05: Applications to actuarial sciences and financial mathematics
Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 2 , June 2017 , pp. 490 - 506
Copyright
Copyright © Applied Probability Trust 2017 

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