The calculation of expectations for classes of diffusion processes by lie symmetry methods

Craddock, M; Lennox, KA

The calculation of expectations for classes of diffusion processes by lie symmetry methods

Craddock, M Lennox, KA

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Publication Type:: Journal Article
Citation:: Annals of Applied Probability, 2009, 19 (1), pp. 127 - 157
Issue Date:: 2009-02-01

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Field	Value	Language
dc.contributor.author	Craddock, M	en_US
dc.contributor.author	Lennox, KA	en_US
dc.date.issued	2009-02-01	en_US
dc.identifier.citation	Annals of Applied Probability, 2009, 19 (1), pp. 127 - 157	en_US
dc.identifier.issn	1050-5164	en_US
dc.identifier.uri	http://hdl.handle.net/10453/8295
dc.description.abstract	This paper uses Lie symmetry methods to calculate certain expectations for a large class of Itô diffusions. We show that if the problem has sufficient symmetry, then the problem of computing functionals of the form Ex(e-λxt-∫t0 g(Xs)ds) can be reduced to evaluating a single integral of known functions. Given a drift f we determine the functions g for which the corresponding functional can be calculated by symmetry. Conversely, given g, we can determine precisely those drifts f for which the transition density and the functional may be computed by symmetry. Many examples are presented to illustrate the method. © Institute of Mathematical Statistics, 2009.	en_US
dc.relation.ispartof	Annals of Applied Probability	en_US
dc.relation.isbasedon	10.1214/08-AAP534	en_US
dc.subject.classification	Statistics & Probability	en_US
dc.title	The calculation of expectations for classes of diffusion processes by lie symmetry methods	en_US
dc.type	Journal Article
utslib.citation.volume	1	en_US
utslib.citation.volume	19	en_US
utslib.for	010404 Probability Theory	en_US
utslib.for	0102 Applied Mathematics	en_US
utslib.for	0104 Statistics	en_US
dc.location.activity	ISI:000264247900006	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
pubs.organisational-group	/University of Technology Sydney/Strength - QFRC - Quantitative Finance Research Centre
utslib.copyright.status	open_access
pubs.issue	1	en_US
pubs.publication-status	Published	en_US
pubs.volume	19	en_US

Abstract:

This paper uses Lie symmetry methods to calculate certain expectations for a large class of Itô diffusions. We show that if the problem has sufficient symmetry, then the problem of computing functionals of the form Ex(e-λxt-∫t0 g(Xs)ds) can be reduced to evaluating a single integral of known functions. Given a drift f we determine the functions g for which the corresponding functional can be calculated by symmetry. Conversely, given g, we can determine precisely those drifts f for which the transition density and the functional may be computed by symmetry. Many examples are presented to illustrate the method. © Institute of Mathematical Statistics, 2009.

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http://hdl.handle.net/10453/8295