Enlargement of filtrations with random times for processes with jumps
type: Item
instance of: scholarly article
title: Enlargement of filtrations with random times for processes with jumps
zbMATH Open document ID: 1157.60040
author: Arturo Kohatsu-Higa
author: Makoto Yamazato
published in: Stochastic Processes and their Applications
publication date: 2008-08-22T00:00:00Z
review text: The main purpose of the present paper is to extend a result due to \textit{J. Jacod} [Lect. Notes Math. 1118, 15--35 (1985; Zbl 0568.60049)] on the initial enlargement of filtrations with respect to random times. In Jacod's theorem it is assumed that the conditional distribution of the random time is absolutely continuous with respect to a nonrandom measure. Motivated by examples in the theory of insider trading the authors obtain extensions of Jacod's theorem where the reference measure mentioned above can be random. In the desired extension, the decomposition of the semimartingale (in the enlarged filtration) contains an extra term. An example concerns an insider who knows the time of the nth jump of the stock price of size bigger than a certain number. Another example is concerning the random time of the last jump before \(T\) of absolute size bigger than a given number (which is not a stopping time). These situations are not covered by Jacod's theorem.
reviewed by: Klaus Schürger
Mathematics Subject Classification ID: 60G48
Mathematics Subject Classification ID: 60G35
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 91B28
Mathematics Subject Classification ID: 60G57
zbMATH DE Number: 5315299
zbMATH Keywords: semimartingale
zbMATH Keywords: Lévy processes
zbMATH Keywords: enlargement of filtrations
zbMATH Keywords: random times
zbMATH Keywords: Jacod's theorem
MaRDI profile type: Publication
full work available at URL: j.spa.2007.07.014
OpenAlex ID: W2030465282
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DOI: 10.1016/J.SPA.2007.07.014
description: scientific article; zbMATH DE number 5315299