# On Exponential Functionals of Brownian Motion and Related Processes

by Marc Yor

Publisher: Springer

Written in English ## Subjects:

• Finance,
• Functional analysis,
• Probability & statistics,
• Mathematics,
• Markov Processes,
• Science/Mathematics,
• Probability & Statistics - General,
• Applied,
• Asian options,
• Bessel functions,
• Bessel processes,
• Geometric Brownian motion,
• Mathematics / Statistics,
• beta-gamma variables,
• Brownian motion processes,
• Mathematical models
The Physical Object
FormatPaperback
Number of Pages203
ID Numbers
Open LibraryOL9062974M
ISBN 103540659439
ISBN 109783540659433

Asymptotic results for exponential functionals of Levy processes´ A book on CB-processes with competition (nonlinear branching): First Prev Next Last Go Back Full Screen Close Quit 5. Random environments gis a Brownian motion (if = 1) or a spectrally positive (1+)-stable. A geometric Brownian motion (GBM) (also known as exponential Brownian motion) is a continuous-time stochastic process in which the logarithm of the randomly varying quantity follows a Brownian motion (also called a Wiener process) with drift. It is an important example of stochastic processes satisfying a stochastic differential equation (SDE); in particular, it is used in mathematical finance. Brownian motion with drift. So far we considered a Brownian motion which is characterized by zero mean and some variance parameter σ. 2. The standard Brownian motion is the special case σ = 1. There is a natural way to extend this process to a non-zero mean process by considering B µ(t) = µt + B(t), given a Brownian motion B(t). Some.   The integral of geometric Brownian motion - Volume 33 Issue 1 - Daniel Dufresne On the distribution and asymptotic results for exponential functionals of Lévy processes. In Exponential Functionals and Principal Values Related to Brownian Motion, ed. Yor, by:

Naturally, when certain problems originating from financial mathematics concerning exponential functionals of Brownian motion were brought to his attention, Marc immediately got interested. These problems led him to subsequently focus attention on exponential functionals of Lévy processes, and to other problems involving Brownian motion that. Asymptotic behaviour of exponential functionals of L evy processes with applications to random processes in random environment Sandra Palau, Juan Carlos Pardo and Charline Smadi Centro de Investigaci on en Matem aticas A.C. Calle Jalisco s/n. Guanajuato, M exico. E-mail address: f , jcpardo g @ Size: KB. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. Sign up to join this community. Mean of exponential Brownian motion. Ask Question Asked 4 years, 4 . ometric Brownian process, i.e., the logarithm of the rate at the end of a branch is normally distributed with mean set to the logarithm of the rate at the beginning of the branch, and variance proportional to the time elapsed along that edge. Mean reverting stochastic processes such as the Ornstein-Uhlenbeck process or the Cox-.

Buy Aspects of Brownian Motion (Universitext) by Roger Mansuy (ISBN: ) from Amazon's Book Store. Everyday low prices and free delivery on eligible orders. [] M., Yor, Exponential Functionals of Brownian Motion and Related Processes, Springer-Verlag, [] M., Yor, Sur la continuité des temps locaux associés à certaines semimartingales, Astérisque 52–53 (), 23–Cited by: 3. Springer, p. ISBN: , e-ISBN: Series: Universitext. Stochastic calculus and excursion theory are very efficient tools for obtaining either exact or asymptotic results about Brownian motion and related processes. This book focuses on special classes of. Exponential functionals of Brownian motion, II: Some related diffusion processes. This is the second part of our survey on exponential functionals of Brownian motion. We focus on the applications of the results about the distributions of the exponential functionals, which have been discussed in the first part. Author: Hiroyuki Matsumoto and Marc Yor.

## On Exponential Functionals of Brownian Motion and Related Processes by Marc Yor Download PDF EPUB FB2

This volume collects papers about the laws of geometric Brownian motions and their time-integrals, written by the author and coauthors between and These functionals play an important role in Mathematical Finance, as well as in (probabilistic) studies related Cited by: Exponential Functionals of Brownian Motion and Related Processes (Springer Finance) - Kindle edition by Marc Yor.

Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Exponential Functionals of Brownian Motion and Related Processes (Springer Finance).

This monograph contains: ten papers written by the author, and co-authors, between December and October 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.

: Springer-Verlag Berlin Heidelberg. 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 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.

This volume collects papers about the laws of geometric Brownian motions and their time-integrals, written by the author and coauthors between and Throughout the volume, connections with more recent studies involving exponential functionals of Lévy processes Author: Marc Yor.

Abstract. In this paper, distributional questions which arise in certain mathematical finance models are studied: the distribution of the integral over a fixed time interval [0, T]of the exponential of Brownian motion with drift is computed explicitly, with the help of computations previously made by the author for Bessel moments of this integral are obtained independently and Cited by: Exponential functionals of Brownian motion, II: Some related diﬀusion processes∗ Hiroyuki Matsumoto Graduate School of Information Science, Nagoya University, Chikusa-ku, NagoyaJapan e-mail: [email protected] Marc Yor Laboratoire de Probabilit´es and Institut universitaire de France, Universit´e Pierre et Marie Curie.

There are two parts in this book. The first part is devoted mainly to the proper­ ties of linear diffusions in general and Brownian motion in particular. The second part consists of tables of distributions of functionals of Brownian motion and re­ lated processes. The primary aim of this book is to.

ON DISTRIBUTIONS OF EXPONENTIAL FUNCTIONALS OF THE PROCESSES WITH INDEPENDENT INCREMENTS L. Vostrikova, LAREMA, D´epartement de Math´ematiques, Universit´e d’Angers, 2, Bd LavoisierAngers Cedex01 Abstract. The aim of this paper is to study the laws of the ex-ponential functionals of the processes X with independent incre-ments.

Download Citation | Exponential Functionals of Brownian Motion and Related Processes | 0. Functionals of Brownian Motion in Finance and in Insurance.- 1.

On Certain Exponential Functionals Author: Marc Yor. from book Exponential Functionals of Brownian Motion and Related Processes (pp) On Some Exponential Functionals of Brownian Motion Chapter February with 65 ReadsAuthor: Marc Yor.

OnSomeExponential Functionals ofBrownianMotion Marc Yor Universite P. et M. Curie-Laboratoire de Probabilit6s Tour56 3" Etage - 4, Place Jussieu - Paris cedex 05 Abstract: In this paper, distributional questions which arise in certain Mathematical Finance models are studied: the distribution of the integral over a fixed time interval {0,T} of the exponential of Brownian motion with drift File Size: 1MB.

Title: Exponential functionals of Brownian motion, II: Some related diffusion processes Authors: Hiroyuki Matsumoto, Marc Yor (Submitted on 21 Nov ( Cited by: 4. The Laws of Exponential Functionals of Brownian Motion, Taken at Various Random Times 55 C.R.

Acad. Sci., Pans, Sir. 7 (), 5. Bessel Processes, Asian Options, and Perpetuities 63 Mathematical Finance, Vol. 3, No. 4 (October ), (with Helyette Geman) 6. Further Results on Exponential Functionals of Brownian Motion 93 7. Exponential stopping 90 3. Stopping at first exit time 94 4.

Stopping at inverse additive functional 97 Appendix 1. Briefly on some diffusions Part II: TABLES OF DISTRIBUTIONS OF FUNCTIONALS OF BROWNIAN MOTION AND RELATED PROCESSES Introduction 1.

List of functionals 2. Comments and references 1. Brownian motion 1. Exponential. Exponential functionals of Brownian motion, II: Some related di usion processes Hiroyuki Matsumoto Graduate School of Information Science, Nagoya University, Chikusa-ku, NagoyaJapan e-mail: [email protected] Marc Yor Laboratoire de Probabilit es and Institut universitaire de France, Universit e Pierre et Marie Curie.

Highlights A surprising new application of approximation theory to exponential Brownian motion is provided. Correlation coefficient for exponential Brownian motion and time average is calculated.

We demonstrate that the moments of the time average are divided differences of the exponential function. We also prove that the moments agree with the more complex formulae obtained by Oshanin and by: 6.

A guide to Brownian motion and related stochastic processes Jim Pitman and Marc Yor Dept. Statistics, University of California, Evans Hall #Berkeley, CAUSA e-mail: [email protected] Abstract: This is a guide to the mathematical theory of Brownian mo-tion and related stochastic processes, with indications of how this.

Stochastic calculus and excursion theory are very efficient tools to obtain either exact or asymptotic results about Brownian motion and related processes.

The emphasis of this book is on special classes of such Brownian functionals as: Gaussian subspaces of the Gaussian space of Brownian motion; - Brownian quadratic funtionals.

Let B={Bt}t≥0 be a one-dimensional standard Brownian motion, to which we associate the exponential additive functional At=∫0te2Bsds,t≥0. Starting from. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields.

It only takes a minute to sign up. Browse other questions tagged exponential-function brownian-motion martingales or ask your own question. Show that a process is Brownian motion.

This is the second part of our survey on exponential functionals of Brownian motion. We focus on the applications of the results about the distributions of the exponential functionals, which have been discussed in the first part.

Hiroyuki; Yor, Marc. Exponential functionals of Brownian motion, II: Some related diffusion processes. Probab Cited by: Exponential functionals of Brownian motion, I: Probability laws at xed time Hiroyuki Matsumoto Graduate School of Information Science, Nagoya University, Chikusa-ku, NagoyaJapan e-mail: [email protected] Marc Yor Laboratoire de Probabilit es and Institut universitaire de France, Universit e Pierre et Marie Curie.

Beta-gamma algebra identities and Lie-theoretic exponential functionals of Brownian motion Chhaibi, Reda, Electronic Journal of Probability, ; Exponential functionals of Brownian motion, II: Some related diffusion processes Matsumoto, Hiroyuki and Yor, Marc, Probability Surveys, ; Boundary Crossing Probabilities and Statistical Applications Siegmund, David, The Annals of Statistics, Description: Stochastic calculus and excursion theory are very efficient tools for obtaining either exact or asymptotic results about Brownian motion and related processes.

This book focuses on special classes of Brownian functionals, including Gaussian subspaces of the Gaussian space of Brownian motion; Brownian quadratic funtionals; Brownian. Several of his beautiful papers on this topic may be found in his book: Exponential functionals of Brownian motion and related processes.

Though motivated by mathematical finance, it is interesting. Marc Yor (24 July – 9 January ) was a French mathematician well known for his work on stochastic processes, especially properties of semimartingales, Brownian motion and other Lévy processes, the Bessel processes, and their applications to mathematical : Mathematics.

Stochastic calculus and excursion theory are very efficient tools for obtaining either exact or asymptotic results about Brownian motion and related processes. This book focuses on special classes of Brownian functionals, including Gaussian subspaces of the Gaussian space of Brownian motion; Brownian quadratic funtionals; Brownian local times.

Exponential Functionals of Brownian Motion and Related Processes. Summary: This volume collects papers about the laws of geometric Brownian motions and their time-integrals, written by the author and coauthors between and Functionals of Brownian motion in finance and in insurance / Hélyette Geman --On certain exponential functionals of real-valued Brownian motion / Marc Yor --On some exponential functionals of Brownian motion / Marc Yor --Some relations between Bessel processes, Asian options and confluent hypergeometric functions / Marc Yor and Hélyette Geman.

() On ladder height densities and Laguerre series in the study of stochastic functionals. II. Exponential functionals of brownian motion and asian option values.

Advances in Applied ProbabilityCited by:   Several of his beautiful papers on this topic may be found in his book: Exponential functionals of Brownian motion and related processes. Though motivated by mathematical finance, it is interesting that exponential functionals have been found to have connections with representation theory of Lie groups and integrable systems (see also this paper).In this paper, distributional questions which arise in certain mathematical finance models are studied: the distribution of the integral over a fixed time interval [0, T]of the exponential of Brownian motion with drift is computed explicitly, with the help of computations previously made by the author for Bessel processes.

The moments of this integral are obtained independently and take a.