Some absolute continuity relationships for certain anticipative transformations of geometric Brownian motions.
type: Item
instance of: scholarly article
title: Some absolute continuity relationships for certain anticipative transformations of geometric Brownian motions.
zbMATH Open document ID: 1033.60085
author: Catherine Donati-Martin
author: Hiroyuki Matsumoto
author: Marc Yor
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 2004-03-20T00:00:00Z
review text: The authors discuss the anticipative transform of a geometric Brownian motion and its relative properties, such as the characterization of this transform, the filtrations, generalized Dufresne's identity, etc. Further, the absolute continuity relationships between the law of the geometric Brownian motion and its images by the transform is presented. Finally, the aforementioned results are used for studying the solutions for some certain stochastic differential equations with anticipative drifts, pseudo martingale properties and anticipative change of probability measure.
reviewed by: Ching-Tang Wu
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 1744039
zbMATH Keywords: geometric Brownian motion
zbMATH Keywords: stochastic differential equation
zbMATH Keywords: anticipative transformation
zbMATH Keywords: Dufresne's identity
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1145477226
OpenAlex ID: W2003732173
cites work: Nonexistence of strong nonanticipating solutions to stochastic DEs: implications for functional DEs, filtering, and control
cites work: Realizing a weak solution on a probability space
cites work: A conditional approach to the anticipating Girsanov transformation
cites work: Equations différentielles stochastiques dans avec conditions aux bords
cites work: The Distribution of a Perpetuity, with Applications to Risk Theory and Pension Funding
cites work: An affine property of the reciprocal Asian option process
cites work: Anticipation cancelled by a Girsanov transformation: A paradox on Wiener space
cites work: Q3038308
cites work: Q4139359
cites work: A version of Pitman's 2M — X theorem for geometric Brownian motions
cites work: A relationship between Brownian motions with opposite drifts via certain enlargements of the Brownian filtration
cites work: An analogue of Pitman’s 2M – X theorem for exponential Wiener functionals: Part I: A time-inversion approach
DOI: 10.2977/PRIMS/1145477226
description: scientific article; zbMATH DE number 1744039