Jesper Lund Pedersen,
	
Prediction of the ultimate maximum of Brownian motion

Abstract:
The focus of this talk will be on optimal prediction of the
ultimate maximum of a Brownian motion. At time 0 we start to observe a
Brownian path. Based upon the information which is continuously
updated through the observation of the path, a (stopping) time is
determined such that the path is as close as possible to its unknown
ultimate maximum (over a given time interval). The closeness is
measured by a q-mean and a probability distance. Formally this can be
formulated as an optimal stopping problem.