Rare event simulation for diffusion processes via two-stage importance sampling

Metzler Adam () and Scott Alexandre ()
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Metzler Adam: Wilfrid Laurier University, 75 University Avenue West, Waterloo, Ontario, Canada
Scott Alexandre: Western University, 1151 Richmond Street North, London, Ontario, Canada

Monte Carlo Methods and Applications, 2014, vol. 20, issue 2, 77-100

Abstract: We consider the problem of estimating expected values of functionals of real-valued diffusions over regions in path space that have very small probability. We propose a two-stage importance sampling procedure that first converts the problem into one involving standard Brownian motion and then addresses the rare event problem in this simpler setting. In order to identify an effective yet practical importance measure we propose using a time-dependent deterministic drift that minimizes the relative entropy between the corresponding importance measure and the conditional law of the standard Brownian motion, given that its trajectory lies in the region of interest. We provide numerical evidence that (i) our entropy-based criteria performs favourably with an alternative, but less general and less practical, criteria based on large deviations and (ii) our two-stage procedure performs admirably in cases where the region of interest is so rare that crude estimators fail completely.

Keywords: Importance sampling; diffusion processes; rare events; cross entropy; Brownian motion (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1515/mcma-2013-0019

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