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On the exact and ε-strong simulation of (jump) diffusions
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Pollock, Murray, Johansen, Adam M. and Roberts, Gareth O. (2016) On the exact and ε-strong simulation of (jump) diffusions. Bernoulli, 22 (2). pp. 794-856. doi:10.3150/14-BEJ676 ISSN 1350-7265.
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Official URL: http://dx.doi.org/10.3150/14-BEJ676
Abstract
This paper introduces a framework for simulating finite dimensional representations of (jump) diffusion sample paths over finite intervals, without discretisation error (exactly), in such a way that the sample path can be restored at any finite collection of time points. Within this framework we extend existing exact algorithms and introduce novel adaptive approaches. We consider an application of the methodology developed within this paper which allows the simulation of upper and lower bounding processes which almost surely constrain (jump) diffusion sample paths to any specified tolerance. We demonstrate the efficacy of our approach by showing that with finite computation it is possible to determine whether or not sample paths cross various irregular barriers, simulate to any specified tolerance the first hitting time of the irregular barrier and simulate killed diffusion sample paths.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
Library of Congress Subject Headings (LCSH): | Algorithms, Probabilities, Perfect simulation (Statistics) | ||||||||
Journal or Publication Title: | Bernoulli | ||||||||
Publisher: | Int Statistical Institute | ||||||||
ISSN: | 1350-7265 | ||||||||
Official Date: | May 2016 | ||||||||
Dates: |
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Volume: | 22 | ||||||||
Number: | 2 | ||||||||
Page Range: | pp. 794-856 | ||||||||
DOI: | 10.3150/14-BEJ676 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||
Date of first compliant deposit: | 31 May 2016 | ||||||||
Date of first compliant Open Access: | 31 May 2016 | ||||||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC) | ||||||||
Grant number: | EP/P50516X/1, EP/1017984/1, EP/G026521/1, EP/D002060/1. | ||||||||
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