Optimal Prediction: An overview of the history, applications, and potential directions
Actuarial Specialist / Program Coordinator
Department of Mathematics
Michigan State University
Optimal prediction is about a decade old now, but has fast become one of the most exciting new areas in Optimal Stopping. The original paper by Graversen, Peskir, and Shiryaev showed, in an elegantly simple way, that one could compute the best time to stop a Brownian motion "as close as possible" to its ultimate maximum over a finite time interval.
Since then, researchers have worked to extend this idea to other diffusions, different measures of "close", and to financial applications.
In this talk, we review the original approach, extensions, and current research including the recent application to infinite horizon prediction
The area is rich with potential for new research, and it is hoped that young mathematicians will be encouraged to read more on the subject after this talk.