第1５回デリバティブ部会セミナー

投稿日: 2015/05/27 11:13:08

日時：2015年7月24日(金曜) 19:00- 20:00

場所：立命館大学東京キャンパス（サピアタワー8F )

講師：Erik Baurdoux (London School of Economics)

講演タイトル：Optimal prediction of the time of the ultimate maximum

講演概要:Optimal prediction of the ultimate maximum is a non-standard optimal stopping problem in the sense that the pay-off function depends on a process which is not adapted to the filtration at hand.  Our aim is to approximate by stopping times as close as possible the (random) time of the ultimate maximum. For a finite time horizon, this problem has been studied in various papers, including Du Toit, J. and Peskir, G. (AAP 2009) and Bernyk, V., Dalang, R.C. and Peskir, G. (Ann. Probab. 2011) for a Brownian motion and one-sided stable process, respectively. In this talk we will discuss the infinite horizon problem for two classes of processes. On the one hand we consider a general Lévy process and we find an optimal stopping time as a first passage time of the process reflected at its supremum. On the other hand, we will see that for positive self-similar Markov processes the Lamperti transform allows us to consider it as an optimal stopping problem in a Lévy setting. This talk is based on joint work with Dr. Kees van Schaik and with Andreas Kyprianou and Curdin Ott in the Lévy and positive self-similar case, respectively.