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On the threshold strategies in optimal stopping problems for diffusion processes

Part of: Stochastic processes Markov processes

Published online by Cambridge University Press:  15 September 2017

Vadim Arkin  and
Alexander Slastnikov
Vadim Arkin*
Affiliation:
Central Economics and Mathematics Institute
Alexander Slastnikov*
Affiliation:
Central Economics and Mathematics Institute
*
* Postal address: Central Economics and Mathematics Institute, Nakhimovskii pr., 47, Moscow, 117418, Russia.
* Postal address: Central Economics and Mathematics Institute, Nakhimovskii pr., 47, Moscow, 117418, Russia.
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Abstract

We study a problem when the optimal stopping for a one-dimensional diffusion process is generated by a threshold strategy. Namely, we give necessary and sufficient conditions (on the diffusion process and the payoff function) under which a stopping set has a threshold structure.

Keywords

Diffusion processoptimal stoppingstopping setthreshold structure

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 60J60: Diffusion processes
Type
Short Communications
Information
Journal of Applied Probability , Volume 54 , Issue 3 , September 2017 , pp. 963 - 969
Copyright
Copyright © Applied Probability Trust 2017 

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References

[1] Arkin, V. I. (2015). Threshold strategies in optimal stopping problem for one-dimensional diffusion processes. Theory Prob. Appl. 59, 311–319. CrossRefGoogle Scholar
[2] Borodin, A. N. and Salminen, P. (2002). Handbook of Brownian Motion—Facts and Formulae, 2nd edn. Birkhäuser, Basel. CrossRefGoogle Scholar
[3] Crocce, F. and Mordecki, E. (2014). Explicit solutions in one-sided optimal stopping problems for one-dimensional diffusions. Stochastics 86, 491–509. Google Scholar
[4] Dayanik, S. and Karatzas, I. (2003). On the optimal stopping problem for one-dimensional diffusions. Stoch. Process. Appl. 107, 173–212. Google Scholar
[5] Karatzas, I. and Shreve, S. E. (1988). Brownian Motion and Stochastic Calculus. Springer, New York. Google Scholar
[6] Lamberton, D. and Zervos, M. (2013). On the optimal stopping of one-dimensional diffusion. Electron. J. Prob. 18, 34. Google Scholar
[7] Villeneuve, S. (2007). On threshold strategies and the smooth-fit principle for optimal stopping problems. J. Appl. Prob. 44, 181–198. Google Scholar