Random Times And Enlargements Of Filtrations In A Brownian Setting

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Random Times And Enlargements Of Filtrations In A Brownian Setting

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Author : Roger Mansuy
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-02-10

Random Times And Enlargements Of Filtrations In A Brownian Setting written by Roger Mansuy and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-10 with Mathematics categories.

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 Azéma-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 progressive kind. It is accessible to researchers and graduate students working in stochastic calculus and excursion theory, and more broadly to mathematicians acquainted with the basics of Brownian motion.

Enlargement Of Filtration With Finance In View

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Author : Anna Aksamit
language : en
Publisher: Springer
Release Date : 2017-11-18

Enlargement Of Filtration With Finance In View written by Anna Aksamit and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-18 with Mathematics categories.

This volume presents classical results of the theory of enlargement of filtration. The focus is on the behavior of martingales with respect to the enlarged filtration and related objects. The study is conducted in various contexts including immersion, progressive enlargement with a random time and initial enlargement with a random variable. The aim of this book is to collect the main mathematical results (with proofs) previously spread among numerous papers, great part of which is only available in French. Many examples and applications to finance, in particular to credit risk modelling and the study of asymmetric information, are provided to illustrate the theory. A detailed summary of further connections and applications is given in bibliographic notes which enables to deepen study of the topic. This book fills a gap in the literature and serves as a guide for graduate students and researchers interested in the role of information in financial mathematics and in econometric science. A basic knowledge of the general theory of stochastic processes is assumed as a prerequisite.

Local Times And Excursion Theory For Brownian Motion

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Author : Ju-Yi Yen
language : en
Publisher: Springer
Release Date : 2013-10-01

Local Times And Excursion Theory For Brownian Motion written by Ju-Yi Yen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-01 with Mathematics categories.

This monograph discusses the existence and regularity properties of local times associated to a continuous semimartingale, as well as excursion theory for Brownian paths. Realizations of Brownian excursion processes may be translated in terms of the realizations of a Wiener process under certain conditions. With this aim in mind, the monograph presents applications to topics which are not usually treated with the same tools, e.g.: arc sine law, laws of functionals of Brownian motion, and the Feynman-Kac formula.

Option Prices As Probabilities

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Author : Christophe Profeta
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-26

Option Prices As Probabilities written by Christophe Profeta and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-26 with Mathematics categories.

Discovered in the seventies, Black-Scholes formula continues to play a central role in Mathematical Finance. We recall this formula. Let (B ,t? 0; F ,t? 0, P) - t t note a standard Brownian motion with B = 0, (F ,t? 0) being its natural ?ltra- 0 t t tion. Let E := exp B? ,t? 0 denote the exponential martingale associated t t 2 to (B ,t? 0). This martingale, also called geometric Brownian motion, is a model t to describe the evolution of prices of a risky asset. Let, for every K? 0: + ? (t) :=E (K?E ) (0.1) K t and + C (t) :=E (E?K) (0.2) K t denote respectively the price of a European put, resp. of a European call, associated with this martingale. Let N be the cumulative distribution function of a reduced Gaussian variable: x 2 y 1 ? 2 ? N (x) := e dy. (0.3) 2? ?? The celebrated Black-Scholes formula gives an explicit expression of? (t) and K C (t) in terms ofN : K ? ? log(K) t log(K) t ? (t)= KN ? + ?N ? ? (0.4) K t 2 t 2 and ? ?

Penalising Brownian Paths

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Author : Bernard Roynette
language : en
Publisher: Springer
Release Date : 2009-07-31

Penalising Brownian Paths written by Bernard Roynette and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-31 with Mathematics categories.

Penalising a process is to modify its distribution with a limiting procedure, thus defining a new process whose properties differ somewhat from those of the original one. We are presenting a number of examples of such penalisations in the Brownian and Bessel processes framework. The Martingale theory plays a crucial role. A general principle for penalisation emerges from these examples. In particular, it is shown in the Brownian framework that a positive sigma-finite measure takes a large class of penalisations into account.

Aspects Of Brownian Motion

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Author : Roger Mansuy
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-16

Aspects Of Brownian Motion written by Roger Mansuy and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-16 with Mathematics categories.

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 with drift; Time spent by Brownian motion below a multiple of its one-sided supremum.

S Minaire De Probabilit S Xliv

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Author : Catherine Donati-Martin
language : en
Publisher: Springer
Release Date : 2012-05-12

S Minaire De Probabilit S Xliv written by Catherine Donati-Martin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-12 with Mathematics categories.

As usual, some of the contributions to this 44th Séminaire de Probabilités were presented during the Journées de Probabilités held in Dijon in June 2010. The remainder were spontaneous submissions or were solicited by the editors. The traditional and historical themes of the Séminaire are covered, such as stochastic calculus, local times and excursions, and martingales. Some subjects already touched on in the previous volumes are still here: free probability, rough paths, limit theorems for general processes (here fractional Brownian motion and polymers), and large deviations. Lastly, this volume explores new topics, including variable length Markov chains and peacocks. We hope that the whole volume is a good sample of the main streams of current research on probability and stochastic processes, in particular those active in France.

Contemporary Quantitative Finance

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Author : Carl Chiarella
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-23

Contemporary Quantitative Finance written by Carl Chiarella and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-23 with Mathematics categories.

This volume contains a collection of papers dedicated to Professor Eckhard Platen to celebrate his 60th birthday, which occurred in 2009. The contributions have been written by a number of his colleagues and co-authors. All papers have been - viewed and presented as keynote talks at the international conference “Quantitative Methods in Finance” (QMF) in Sydney in December 2009. The QMF Conference Series was initiated by Eckhard Platen in 1993 when he was at the Australian - tional University (ANU) in Canberra. Since joining UTS in 1997 the conference came to be organised on a much larger scale and has grown to become a signi?cant international event in quantitative ?nance. Professor Platen has held the Chair of Quantitative Finance at the University of Technology, Sydney (UTS) jointly in the Faculties of Business and Science since 1997. Prior to this appointment, he was the Founding Head of the Centre for Fin- cial Mathematics at the Institute of Advanced Studies at ANU, a position to which he was appointed in 1994. Eckhard completed a PhD in Mathematics at the Technical University in Dresden in 1975 and in 1985 obtained his Doctor of Science degree (Habilitation degree in the German system) from the Academy of Sciences in Berlin where he headed the Stochastics group at the Weierstrass Institute.

Stochastic Calculus Via Regularizations

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Author : Francesco Russo
language : en
Publisher: Springer Nature
Release Date : 2022-11-15

Stochastic Calculus Via Regularizations written by Francesco Russo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-15 with Mathematics categories.

The book constitutes an introduction to stochastic calculus, stochastic differential equations and related topics such as Malliavin calculus. On the other hand it focuses on the techniques of stochastic integration and calculus via regularization initiated by the authors. The definitions relies on a smoothing procedure of the integrator process, they generalize the usual Itô and Stratonovich integrals for Brownian motion but the integrator could also not be a semimartingale and the integrand is allowed to be anticipating. The resulting calculus requires a simple formalism: nevertheless it entails pathwise techniques even though it takes into account randomness. It allows connecting different types of pathwise and non pathwise integrals such as Young, fractional, Skorohod integrals, enlargement of filtration and rough paths. The covariation, but also high order variations, play a fundamental role in the calculus via regularization, which can also be applied for irregular integrators. A large class of Gaussian processes, various generalizations of semimartingales such that Dirichlet and weak Dirichlet processes are revisited. Stochastic calculus via regularization has been successfully used in applications, for instance in robust finance and on modeling vortex filaments in turbulence. The book is addressed to PhD students and researchers in stochastic analysis and applications to various fields.

Portfolio Optimization With Different Information Flow

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Author : Caroline Hillairet
language : en
Publisher: Elsevier
Release Date : 2017-02-10

Portfolio Optimization With Different Information Flow written by Caroline Hillairet and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-10 with Business & Economics categories.

Portfolio Optimization with Different Information Flow recalls the stochastic tools and results concerning the stochastic optimization theory and the enlargement filtration theory.The authors apply the theory of the enlargement of filtrations and solve the optimization problem. Two main types of enlargement of filtration are discussed: initial and progressive, using tools from various fields, such as from stochastic calculus and convex analysis, optimal stochastic control and backward stochastic differential equations. This theoretical and numerical analysis is applied in different market settings to provide a good basis for the understanding of portfolio optimization with different information flow. - Presents recent progress of stochastic portfolio optimization with exotic filtrations - Shows you how to apply the tools of the enlargement of filtrations to resolve the optimization problem - Uses tools from various fields from enlargement of filtration theory, stochastic calculus, convex analysis, optimal stochastic control, and backward stochastic differential equations