Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/25140
Authors: 
Gapeev, Pavel V.
Year of Publication: 
2006
Series/Report no.: 
SFB 649 discussion paper 2006,057
Abstract: 
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 surface 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.
Document Type: 
Working Paper

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