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2006 Discounted optimal stopping for maxima in diffusion models with finite horizon
Pavel Gapeev
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Electron. J. Probab. 11: 1031-1048 (2006). DOI: 10.1214/EJP.v11-367


We present a solution to some discounted optimal stopping problem for the maximum of a geometric Brownian motion on a finite time interval. The method of proof is based on reducing the initial optimal stopping problem with the continuation region determined by an increasing continuous boundary surface to a parabolic free-boundary problem. Using the change-of-variable formula with local time on surfaces we show that the optimal boundary can be characterized as a unique solution of a nonlinear integral equation. The result can be interpreted as pricing American fixed-strike lookback option in a diffusion model with finite time horizon.


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Pavel Gapeev. "Discounted optimal stopping for maxima in diffusion models with finite horizon." Electron. J. Probab. 11 1031 - 1048, 2006.


Accepted: 21 November 2006; Published: 2006
First available in Project Euclid: 31 May 2016

zbMATH: 1127.60037
MathSciNet: MR2268535
Digital Object Identifier: 10.1214/EJP.v11-367

Primary: 60G40
Secondary: 35R35 , 45G10 , 60J60 , 91B28

Keywords: a change-of-varia , a nonlinear Volterra integral equation of the second kind , boundary surface , Discounted optimal stopping problem , Finite horizon , Geometric Brownian motion , maximum process , normal reflection , parabolic free-boundary problem , smooth fit


Vol.11 • 2006
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