Open Access
Translator Disclaimer
2010 Parameter-Dependent Optimal Stopping Problems for One-Dimensional Diffusions
Peter Bank, Christoph Baumgarten
Author Affiliations +
Electron. J. Probab. 15: 1971-1993 (2010). DOI: 10.1214/EJP.v15-835


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.


Download Citation

Peter Bank. Christoph Baumgarten. "Parameter-Dependent Optimal Stopping Problems for One-Dimensional Diffusions." Electron. J. Probab. 15 1971 - 1993, 2010.


Accepted: 26 November 2010; Published: 2010
First available in Project Euclid: 1 June 2016

zbMATH: 1226.60057
MathSciNet: MR2745722
Digital Object Identifier: 10.1214/EJP.v15-835

Primary: 60G40
Secondary: 60J60 , 91G20

Keywords: American options , Gittins index , Multi-armed bandit problems , Optimal stopping , universal stopping signal


Vol.15 • 2010
Back to Top