ON THE STOCHASTIC BEHAVIOUR OF OPTIONAL PROCESSES UP TO RANDOM TIMES
成果类型：
Article
署名作者：
Kardaras, Constantinos
署名单位：
University of London; London School Economics & Political Science
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/13-AAP976
发表日期：
2015
页码：
429-464
关键词：
摘要：
In this paper, a study of random times on filtered probability spaces is undertaken. The main message is that, as long as distributional properties of optional processes up to the random time are involved, there is no loss of generality in assuming that the random time is actually a randomised stopping time. This perspective has advantages in both the theoretical and practical study of optional processes up to random times. Applications are given to financial mathematics, as well as to the study of the stochastic behaviour of Brownian motion with drift up to its time of overall maximum as well as up to last-passage times over finite intervals. Furthermore, a novel proof of the Jeulin-Yor decomposition formula via Girsanov's theorem is provided.
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