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Optimal Stopping of a Brownian Bridge

Part of: Stochastic processes Stochastic analysis

Published online by Cambridge University Press:  14 July 2016

Erik Ekström  and
Henrik Wanntorp
Erik Ekström*
Affiliation:
Uppsala University
Henrik Wanntorp*
Affiliation:
Uppsala University
*
∗Postal address: Department of Mathematics, Uppsala University, Box 480, SE-751 06 Uppsala, Sweden.
∗Postal address: Department of Mathematics, Uppsala University, Box 480, SE-751 06 Uppsala, Sweden.
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Abstract

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We study several optimal stopping problems in which the gains process is a Brownian bridge or a functional of a Brownian bridge. Our examples constitute natural finite-horizon optimal stopping problems with explicit solutions.

Keywords

Optimal stoppingBrownian bridge

MSC classification

Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory 60H30: Applications of stochastic analysis (to PDE, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 46 , Issue 1 , March 2009 , pp. 170 - 180
Copyright
Copyright © Applied Probability Trust 2009 

References

[1] Avellaneda, M. and Lipkin, M. D. (2003). A market-induced mechanism for stock pinning. Quant. Finance 3, 417–425.Google Scholar
[2] Crack, T. F. (2007). Heard on the Street: Quantitative Questions from Wall Street Job Interviews. 10th edn.Google Scholar
[3] Pedersen, J. L. and Peskir, G. (2000). Solving non-linear optimal stopping problems by the method of time-change. Stoch. Anal. Appl. 18, 811–835.Google Scholar
[4] Peskir, G. and Shiryaev, A. (2006). Optimal Stopping and Free-Boundary Problems (Lectures Math. ETH Zörich). Birkhöuser, Basel.Google Scholar
[5] Shepp, L. A. (1969). Explicit solutions to some problems of optimal stopping. Ann. Math. Statist. 40, 993–1010.Google Scholar