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Optimal stopping for the exponential of a Brownian bridge
- Publication Year :
- 2020
- Publisher :
- Cambridge University Press, 2020.
-
Abstract
- In this paper we study the problem of stopping a Brownian bridge $X$ in order to maximise the expected value of an exponential gain function. In particular, we solve the stopping problem $$\sup_{0\le \tau\le 1}\mathsf{E}[\mathrm{e}^{X_\tau}]$$ which was posed by Ernst and Shepp in their paper [Commun. Stoch. Anal., 9 (3), 2015, pp. 419--423] 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 develop techniques that use pathwise properties of the Brownian bridge and martingale methods of optimal stopping theory in order to find the optimal stopping rule and to show regularity of the value function.<br />Comment: 22 pages, 6 figures
- Subjects :
- Statistics and Probability
General Mathematics
Structure (category theory)
Expected value
Bond/stock selling
Free boundary problems
01 natural sciences
FOS: Economics and business
010104 statistics & probability
Mathematics::Probability
Bellman equation
Optimal stopping
FOS: Mathematics
Applied mathematics
0101 mathematics
Mathematics - Optimization and Control
Mathematics
Brownian bridge
Continuous boundary
Regularity of value function
010102 general mathematics
Probability (math.PR)
Mathematical Finance (q-fin.MF)
Exponential function
Quantitative Finance - Mathematical Finance
Optimization and Control (math.OC)
Optimal stopping rule
Statistics, Probability and Uncertainty
Martingale (probability theory)
Mathematics - Probability
Subjects
Details
- Language :
- English
- ISSN :
- 00219002
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....3d7a30114d4093301e63c212c0b7fb7f