On the stochastic behaviour of optional processes up to random times

Constantinos Kardaras

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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.

Keywords: Random times; randomised stopping times; times of maximum last; passage times (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Date: 2015-04-01
New Economics Papers: this item is included in nep-ore
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Citations: View citations in EconPapers (6)

Published in Annals of Applied Probability, 1, April, 2015, 25(2), pp. 429-464. ISSN: 1050-5164

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Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:64965

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