Some absolute continuity relationships for certain anticipative transformations of geometric Brownian motions.
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.
scientific article; zbMATH DE number 1744039