State‐dependent importance sampling schemes via minimum cross‐entropy

State‐dependent importance sampling schemes via minimum cross‐entropy

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Article ID: iaor20119384
Volume: 189
Issue: 1
Start Page Number: 357
End Page Number: 388
Publication Date: Sep 2011
Journal: Annals of Operations Research
Authors: ,
Keywords: cross-entropy
Abstract:

We present a method to obtain state‐ and time‐dependent importance sampling estimators by repeatedly solving a minimum cross‐entropy (MCE) program as the simulation progresses. This MCE‐based approach lends a foundation to the natural notion to stop changing the measure when it is no longer needed. We use this method to obtain a state‐ and time‐dependent estimator for the one‐tailed probability of a light‐tailed i.i.d. sum that is logarithmically efficient in general and strongly efficient when the jumps are Gaussian. We go on to construct an estimator for the two‐tailed problem which is shown to be similarly efficient. We consider minor variants of the algorithm obtained via MCE, and present some numerical comparisons between our algorithms and others from the literature.

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