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On the stochastic behaviour of optional processes up to random times

Kardaras, Constantinos (2015) On the stochastic behaviour of optional processes up to random times. Annals of Applied Probability, 25 (2). pp. 429-464. ISSN 1050-5164

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Identification Number: 10.1214/13-AAP976


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.

Item Type: Article
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Additional Information: © 2015 Institute of Mathematical Statistics
Divisions: Statistics
Subjects: H Social Sciences > HA Statistics
Date Deposited: 14 Jan 2016 10:15
Last Modified: 20 Aug 2021 00:30

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