Optimally Stopping of a Brownian Bridge with an Unknown Pinning Time: A Bayesian Approach

Glover, K

Optimally Stopping of a Brownian Bridge with an Unknown Pinning Time: A Bayesian Approach

Glover, K

Permalink

Publisher:: Elsevier
Publication Type:: Journal Article
Citation:: Stochastic Processes and their Applications, 2022, 150, pp. 919-9937
Issue Date:: 2022

Open Access

Copyright Clearance Process

Recently Added
In Progress
Open Access

This item is open access.

Adobe PDF

Download Accepted versionAdobe PDF (455.95 kB)

View on publisher's site

View statistics

Full metadata record

Field	Value	Language
dc.contributor.author	Glover, K https://orcid.org/0000-0002-1518-3482
dc.date.accessioned	2022-06-22T05:49:32Z
dc.date.available	2022-06-22T05:49:32Z
dc.date.issued	2022
dc.identifier.citation	Stochastic Processes and their Applications, 2022, 150, pp. 919-9937
dc.identifier.issn	0304-4149
dc.identifier.uri	http://hdl.handle.net/10453/158318
dc.description.abstract	We consider the problem of optimally stopping a Brownian bridge with an unknown pinning time so as to maximise the value of the process upon stopping. Adopting a Bayesian approach, we assume the stopper has a general continuous prior and is allowed to update their belief about the value of the pinning time through sequential observations of the process. Uncertainty in the pinning time influences both the conditional dynamics of the process and the expected (random) horizon of the optimal stopping problem. We analyse certain gamma and beta distributed priors in detail. Remarkably, the optimal stopping problem in the gamma case becomes time homogeneous and is completely solvable in closed form. Moreover, in the beta case we find that the optimal stopping boundary takes on a square-root form, similar to the classical solution with a known pinning time.
dc.language	en
dc.publisher	Elsevier
dc.relation.ispartof	Stochastic Processes and their Applications
dc.relation.isbasedon	10.1016/j.spa.2020.03.007
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	0102 Applied Mathematics, 0104 Statistics, 1502 Banking, Finance and Investment
dc.subject.classification	Statistics & Probability
dc.title	Optimally Stopping of a Brownian Bridge with an Unknown Pinning Time: A Bayesian Approach
dc.type	Journal Article
utslib.citation.volume	150
utslib.for	0102 Applied Mathematics
utslib.for	0104 Statistics
utslib.for	1502 Banking, Finance and Investment
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/Strength - QFRC - Quantitative Finance Research Centre
utslib.copyright.status	open_access	*
pubs.consider-herdc	true
dc.date.updated	2022-06-22T05:49:31Z
pubs.publication-status	Published
pubs.volume	150

Abstract:

We consider the problem of optimally stopping a Brownian bridge with an unknown pinning time so as to maximise the value of the process upon stopping. Adopting a Bayesian approach, we assume the stopper has a general continuous prior and is allowed to update their belief about the value of the pinning time through sequential observations of the process. Uncertainty in the pinning time influences both the conditional dynamics of the process and the expected (random) horizon of the optimal stopping problem. We analyse certain gamma and beta distributed priors in detail. Remarkably, the optimal stopping problem in the gamma case becomes time homogeneous and is completely solvable in closed form. Moreover, in the beta case we find that the optimal stopping boundary takes on a square-root form, similar to the classical solution with a known pinning time.

Please use this identifier to cite or link to this item:

http://hdl.handle.net/10453/158318