In November 2004, M. Yor and R. Mansuy jointly gave six lectures at Columbia University, New York. These notes follow the contents of that course, covering expansion of filtration formulae; BDG inequalities up to any random time; martingales that vanish on the zero set of Brownian motion; the Azema-Emery martingales and chaos representation; the filtration of truncated Brownian motion; attempts to characterize the Brownian filtration.
The book accordingly sets out to acquaint its readers with the theory and main examples of enlargements of filtrations, of either the initial or the...
In November 2004, M. Yor and R. Mansuy jointly gave six lectures at Columbia University, New York. These notes follow the contents of that course, ...
This monograph contains: - ten papers written by the author, and co-authors, between December 1988 and October 1998 about certain exponential functionals of Brownian motion and related processes, which have been, and still are, of interest, during at least the last decade, to researchers in Mathematical finance; - an introduction to the subject from the view point of Mathematical Finance by H. Geman. The origin of my interest in the study of exponentials of Brownian motion in relation with mathematical finance is the question, first asked to me by S. Jacka in Warwick in December 1988, and...
This monograph contains: - ten papers written by the author, and co-authors, between December 1988 and October 1998 about certain exponential function...
Considering the stupendous gain in importance, in the banking and insurance industries since the early 1990 s, of mathematical methodology, especially probabilistic methodology, it was a very natural idea for the French "Academie des Sciences" to propose a series of public lectures, accessible to an educated audience, to promote a wider understanding for some of the fundamental ideas, techniques and new tools of the financial industries.
These lectures were given at the "Academie des Sciences" in Paris by internationally renowned experts in mathematical finance, and later written up...
Considering the stupendous gain in importance, in the banking and insurance industries since the early 1990 s, of mathematical methodology, especia...
Focuses on topics including expansion of filtration formulae; Burkholder-Gundy inequalities up to any random time; martingales which vanish on the zero set of Brownian motion; the Azema-Emery martingales and chaos representation; the filtration of truncated Brownian motion; and, attempts to characterize the Brownian filtration.
Focuses on topics including expansion of filtration formulae; Burkholder-Gundy inequalities up to any random time; martingales which vanish on the zer...
The different papers contained in this volume are all research papers. The main directions of research which are being developed are: quantum probability, semimartingales and stochastic calculus.
The different papers contained in this volume are all research papers. The main directions of research which are being developed are: quantum probabil...
