De Angelis, T and Milazzo, A (Cover date: March 2020) Optimal stopping for the exponential of a Brownian bridge. Journal of Applied Probability, 57 (1). pp. 361-384. ISSN 0021-9002
Abstract
We study the problem of stopping a Brownian bridge X in order to maximise the expected value of an exponential gain function. The problem was posed by Ernst and Shepp (2015), and was motivated by bond selling with non-negative prices.
Due to the non-linear structure of the exponential gain, we cannot rely on methods used in the literature to find closed-form solutions to other problems involving the Brownian bridge. Instead, we must deal directly with a stopping problem for a time-inhomogeneous diffusion. We develop techniques based on pathwise properties of the Brownian bridge and martingale methods of optimal stopping theory, which allow us to find the optimal stopping rule and to show the regularity of the value function.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Applied Probability Trust 2020. This article has been published in a revised form in Journal of Applied Probability, http://doi.org/10.1017/jpr.2019.98. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. |
Keywords: | optimal stopping; Brownian bridge; free boundary problems; regularity of value function; continuous boundary; bond/stock selling |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Funding Information: | Funder Grant number EPSRC (Engineering and Physical Sciences Research Council) EP/R021201/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 04 Dec 2019 13:00 |
Last Modified: | 04 Nov 2020 01:39 |
Status: | Published |
Publisher: | Cambridge University Press |
Identification Number: | 10.1017/jpr.2019.98 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:154149 |