M. C. Fu, R. A. Jarrow, Ju-Yi J. Yen, & R. J. Elliott, " Advances in Mathematical Finance "
Birkhuser Boston | 1st edition (July 2007) | ISBN-13: 9780817645458 | 7.6 MB
|“||The technical contributions in the book are divided into three parts. The first part deals with stochastic processes used in mathematical finance, primarily the Levy processes most associated with Dilip, who has been a fervent advocate of this class of processes for addressing the well-known flaws of geometric Brownian motion for asset price modeling. The primary focus is on the Variance-Gamma (VG) process that Dilip and Eugene Seneta introduced to the finance community, and the lead article provides an historical review from the unique vantage point of Dilip’s co-author, starting from the initiation of the collaboration at the University of Sydney. Techniques for simulating the Variance-Gamma process are surveyed in the article by Michael Fu, Dilip’s longtime colleague at Maryland, moving from a review of basic Monte Carlo simulation for the VG process to more advanced topics in variation reduction and efficient estimation of the “Greeks” such as the option delta. The next two pieces by Marc Yor, a longtime close collaborator and the keynote speaker at the birthday conference, provide some mathematical properties and identities for gamma processes and beta and gamma random variables. |
The final article in the first part of the volume, written by frequent collaborator Robert Elliott and his co-author John van der Hoek, reviews the theory of fractional Brownian motion in the white noise framework and provides a new approach for deriving the associated Ito-type stochastic calculus formulas.