On the number of deviations of Geometric Brownian Motion with drift from its extreme points with applications to transaction costs

The number of deviations of a Geometric Brownian Motion with drifts from its extreme points is considered. The properties of these deviations are studied. As an application based on these results, the time instants at which investors decide to buy or sell are examined, when the price of an asset is assumed to follow a Geometric Brownian Motion. Extensions to the modelling of transaction costs are attempted.