確率論セミナー


2018/10/2(Tue)

16:30--18:00 数学教室 大セミナー室 (E404)

Libo Li

University of New South Wales

From Azema supermartingales of nite honest times to optional semimartingales of class-(Sigma)

Given a finite honest time, we derive representations for the additive and multiplicative decomposition of it's Azema supermartingale in terms of optional supermartingales and its running supremum. We then extend the notion of semimartingales of class-(Sigma) to optional semimartingales with jumps in its finite variation part, allowing one to establish formulas similar to the Madan-Roynette-Yor option pricing formulas for larger class of processes. Finally, we introduce the optional multiplicative systems associated with positive submartingales and apply them to construct random times with given Azema supermartingale.