Exponential Functionals of Brownian Motion and Related Processes - Brossura

Yor, Marc

Brossura

ISBN 10: 3540659439 ISBN 13: 9783540659433

Casa editrice: Springer, 2013

Riassunto

This volume collects papers about the laws of geometric Brownian motions and their time-integrals, written by the author and coauthors between 1988 and 1998. Throughout the volume, connections with more recent studies involving exponential functionals of Lévy processes are indicated. Some papers originally published in French are made available in English for the first time.

Su questo libro

Informazioni sull'autore

MARC YOR has been Professor at the Laboratoire de Probabilités et Modèles Aléatoires at the Université Pierre et Marie Curie, Paris, since 1981, and a member of the Académie des Sciences de Paris since 2003. His research interests - which are well illustrated in the present book - bear upon properties of Brownian functionals, either for pure or applied purposes. Recently, Marc Yor has also been working on the interface between number theory and random matrices. ROGER MANSUY has been teaching mathematics at the Lycée Louis le Grand, Paris, since 2006. He has been working with Marc Yor - who was the supervisor of Roger Mansuy's PhD thesis - in recent years. Prior to the present volume he and Marc Yor collaborated in publishing volume 1873 of the series Lecture Notes in Mathematics entitled "Random Times and Enlargements of Filtration in a Brownian setting".

Dalla quarta di copertina

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 later by M. Chesney in Geneva, and H. Geman in Paris, to compute the price of Asian options, i. e. : to give, as much as possible, an explicit expression for: (1) where A~v) = I~ dsexp2(Bs + liS), with (Bs,s::::: 0) a real-valued Brownian motion. Since the exponential process of Brownian motion with drift, usually called: geometric Brownian motion, may be represented as: t ::::: 0, (2) where (Rt), u ::::: 0) denotes a 15-dimensional Bessel process, with 5 = 2(1I+1), it seemed clear that, starting from (2) [which is analogous to Feller's repre­ sentation of a linear diffusion X in terms of Brownian motion, via the scale function and the speed measure of X], it should be possible to compute quan­ tities related to (1), in particular: in hinging on former computations for Bessel processes.

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 2013
• Lingua: Inglese
• ISBN 10: 3540659439
• ISBN 13: 9783540659433
• Rilegatura: Copertina flessibile
• Numero di pagine: 206
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