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April 2015 On the stochastic behaviour of optional processes up to random times
Constantinos Kardaras
Ann. Appl. Probab. 25(2): 429-464 (April 2015). DOI: 10.1214/13-AAP976

Abstract

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.

Citation

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Constantinos Kardaras. "On the stochastic behaviour of optional processes up to random times." Ann. Appl. Probab. 25 (2) 429 - 464, April 2015. https://doi.org/10.1214/13-AAP976

Information

Published: April 2015
First available in Project Euclid: 19 February 2015

zbMATH: 1316.60057
MathSciNet: MR3313744
Digital Object Identifier: 10.1214/13-AAP976

Subjects:
Primary: 60G07, 60G44

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.25 • No. 2 • April 2015
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