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Optimal double stopping of a Brownian bridge

Part of: Stochastic processes Stochastic analysis

Published online by Cambridge University Press:  21 March 2016

Erik J. Baurdoux ,
Nan Chen ,
Budhi A. Surya  and
Kazutoshi Yamazaki
Erik J. Baurdoux*
Affiliation:
London School of Economics
Nan Chen*
Affiliation:
The Chinese University of Hong Kong
Budhi A. Surya*
Affiliation:
Victoria University of Wellington and Bandung Institute of Technology
Kazutoshi Yamazaki*
Affiliation:
Kansai University
*
∗ Postal address: Department of Statistics, London School of Economics, London WC2A 2AE, UK.
∗∗ Postal address: Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong.
∗∗∗ Postal address: School of Mathematics and Statistics, Victoria University of Wellington, PO Box 600, Wellington 6140, New Zealand.
∗∗∗∗ Postal address: Department of Mathematics, Faculty of Engineering Science, Kansai University, 3-3-35 Yamate-cho Suita, Osaka, 564-8680, Japan. Email address: kyamazak@kansai-u.ac.jp
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Abstract

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We study optimal double stopping problems driven by a Brownian bridge. The objective is to maximize the expected spread between the payoffs achieved at the two stopping times. We study several cases where the solutions can be solved explicitly by strategies of a threshold type.

Keywords

Brownian bridgeoptimal double stoppingbuying-selling strategy

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.)
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 47 , Issue 4 , December 2015 , pp. 1212 - 1234
Copyright
Copyright © Applied Probability Trust 2015 

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