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Parameter-Dependent Optimal Stopping Problems for One-Dimensional Diffusions

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Parameter-Dependent Optimal Stopping Problems for One-Dimensional Diffusions
2.	Creator	Author's name, affiliation, country	Peter Bank; Technische Universität Berlin; Germany
2.	Creator	Author's name, affiliation, country	Christoph Baumgarten; Technische Universität Berlin; Germany
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Optimal stopping, Gittins index, multi-armed bandit problems, American options, universal stopping signal
3.	Subject	Subject classification	60G40, 60J60, 91G20
4.	Description	Abstract	We consider a class of optimal stopping problems for a regular one-dimensional diffusion whose payoff depends on a linear parameter. As shown in Bank and Föllmer (2003) problems of this type may allow for a universal stopping signal that characterizes optimal stopping times for any given parameter via a level-crossing principle of some auxiliary process. For regular one-dimensional diffusions, we provide an explicit construction of this signal in terms of the Laplace transform of level passage times. Explicit solutions are available under certain concavity conditions on the reward function. In general, the construction of the signal at a given point boils down to finding the infimum of an auxiliary function of one real variable. Moreover, we show that monotonicity of the stopping signal corresponds to monotone and concave (in a suitably generalized sense) reward functions. As an application, we show how to extend the construction of Gittins indices of Karatzas (1984) from monotone reward functions to arbitrary functions.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	Quantitative Products Laboratory, Berlin Mathematical School
7.	Date	(YYYY-MM-DD)	2010-11-26
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/835
10.	Identifier	Digital Object Identifier	10.1214/EJP.v15-835
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 15
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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