@article{EJP367,
author = {Pavel Gapeev},
title = {Discounted optimal stopping for maxima in diffusion models with finite horizon},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {11},
year = {2006},
keywords = {Discounted optimal stopping problem; finite horizon; geometric Brownian motion; maximum process; parabolic free-boundary problem; smooth fit; normal reflection; a nonlinear Volterra integral equation of the second kind; boundary surface; a change-of-varia},
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 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.},
pages = {no. 38, 1031-1048},
issn = {1083-6489},
doi = {10.1214/EJP.v11-367},
url = {http://ejp.ejpecp.org/article/view/367}}