On distributions of first passage times and optimal stopping of ar(1) sequences

Novikov, AA

On distributions of first passage times and optimal stopping of ar(1) sequences

Novikov, AA

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Publication Type:: Journal Article
Citation:: Theory of Probability and its Applications, 2009, 53 (3), pp. 419 - 429
Issue Date:: 2009-09-07

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Field	Value	Language
dc.contributor.author	Novikov, AA https://orcid.org/0000-0001-8529-173X	en_US
dc.date.issued	2009-09-07	en_US
dc.identifier.citation	Theory of Probability and its Applications, 2009, 53 (3), pp. 419 - 429	en_US
dc.identifier.issn	0040-585X	en_US
dc.identifier.uri	http://hdl.handle.net/10453/8259
dc.description.abstract	Sufficient conditions for the exponential boundedness of first passage times of autoregressive (AR(1)) sequences are derived in this paper. An identity involving the mean of the first passage time is obtained. Further, this identity is used for finding a logarithmic asymptotic of the mean of the first passage time of Gaussian AR(1)-sequences from a strip. Accuracy of the asymptotic approximation is illustrated by Monte Carlo simulations. A corrected approximation is suggested to improve accuracy of the approximation. An explicit formula is derived for the generating function of the first passage time for the case of AR(1)-sequences generated by an innovation with the exponential distribution. The latter formula is used to study an optimal stopping problem. © 2009 Society for Industrial and Applied Mathematics.	en_US
dc.relation.ispartof	Theory of Probability and its Applications	en_US
dc.relation.isbasedon	10.1137/S0040585X97983730	en_US
dc.subject.classification	Statistics & Probability	en_US
dc.title	On distributions of first passage times and optimal stopping of ar(1) sequences	en_US
dc.type	Journal Article
utslib.citation.volume	3	en_US
utslib.citation.volume	53	en_US
utslib.for	010404 Probability Theory	en_US
utslib.for	0104 Statistics	en_US
dc.location.activity	ISI:000270196500003	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	3	en_US
pubs.publication-status	Published	en_US
pubs.volume	53	en_US

Abstract:

Sufficient conditions for the exponential boundedness of first passage times of autoregressive (AR(1)) sequences are derived in this paper. An identity involving the mean of the first passage time is obtained. Further, this identity is used for finding a logarithmic asymptotic of the mean of the first passage time of Gaussian AR(1)-sequences from a strip. Accuracy of the asymptotic approximation is illustrated by Monte Carlo simulations. A corrected approximation is suggested to improve accuracy of the approximation. An explicit formula is derived for the generating function of the first passage time for the case of AR(1)-sequences generated by an innovation with the exponential distribution. The latter formula is used to study an optimal stopping problem. © 2009 Society for Industrial and Applied Mathematics.

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http://hdl.handle.net/10453/8259