A visual criterion for identifying Ito diffusions as martingales or strict local martingales

Hulley, H; Platen, E

A visual criterion for identifying Ito diffusions as martingales or strict local martingales

Hulley, H

Platen, E

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Publisher:: Springer
Publication Type:: Conference Proceeding
Citation:: Seminar on Stochastic Analysis, Random Fields and Applications VI, 2011, pp. 147 - 157
Issue Date:: 2011-01

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Field	Value	Language
dc.contributor.author	Hulley, H https://orcid.org/0000-0002-6684-8309	en_US
dc.contributor.author	Platen, E https://orcid.org/0000-0003-4595-3123	en_US
dc.contributor.editor	Dalang, R	en_US
dc.contributor.editor	Sozzi, M	en_US
dc.contributor.editor	Russo, F	en_US
dc.date	2008-05-19	en_US
dc.date.issued	2011-01	en_US
dc.identifier.citation	Seminar on Stochastic Analysis, Random Fields and Applications VI, 2011, pp. 147 - 157	en_US
dc.identifier.isbn	978-3-0348-0020-4	en_US
dc.identifier.uri	http://hdl.handle.net/10453/19061
dc.description.abstract	It is often important, in applications of stochastic calculus to financial modelling, to know whether a given local martingale is a martingale or a strict local martingale. We address this problem in the context of a time-homogenous diffusion process with a finite lower boundary, presented as the solution of a driftless stochastic differential equation. Our main theorem demonstrates that the question of whether or not this process is a martingale may be decided simply by examining the slope of a certain increasing function. Further results establish the connection between our theorem and other results in the literature, while a number of examples are provided to illustrate the use of our criterion.	en_US
dc.publisher	Springer	en_US
dc.relation.ispartof	Seminar on Stochastic Analysis, Random Fields and Applications VI	en_US
dc.relation.ispartof	Seminar on Stochastic Processes, Random Fields and Applications	en_US
dc.relation.isbasedon	https://doi.org/10.2139/ssrn.2170276	en_us
dc.rights	This is a post-peer-review, pre-copyedit version of an article published in Seminar on Stochastic Processes, Random Fields and Applications. The final authenticated version is available online at: https://doi.org/10.2139/ssrn.2170276.	en_US
dc.rights	This is a post-peer-review, pre-copyedit version of an article published in Seminar on Stochastic Analysis, Random Fields and Applications VI. The final authenticated version is available online at: https://doi.org/10.2139/ssrn.2170276.	en_US
dc.title	A visual criterion for identifying Ito diffusions as martingales or strict local martingales	en_US
dc.type	Conference Proceeding
utslib.location	Ascona, Switzerland	en_US
utslib.location.activity	Ascona, Switzerland	en_US
utslib.for	010205 Financial Mathematics	en_US
dc.location.activity	Ascona, Switzerland	en_US
dc.location.activity	WOS:000291081400026
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Business
pubs.organisational-group	/University of Technology Sydney/Faculty of Business/Finance Discipline
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.consider-herdc	true	en_US
pubs.finish-date	2008-05-23	en_US
pubs.place-of-publication	Ascona, Switzerland	en_US
pubs.start-date	2008-05-19	en_US

Abstract:

It is often important, in applications of stochastic calculus to financial modelling, to know whether a given local martingale is a martingale or a strict local martingale. We address this problem in the context of a time-homogenous diffusion process with a finite lower boundary, presented as the solution of a driftless stochastic differential equation. Our main theorem demonstrates that the question of whether or not this process is a martingale may be decided simply by examining the slope of a certain increasing function. Further results establish the connection between our theorem and other results in the literature, while a number of examples are provided to illustrate the use of our criterion.

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http://hdl.handle.net/10453/19061