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.
Random Times And Enlargements Of Filtrations
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Author : Libo Li
language : en
Publisher:
Release Date : 2012
Random Times And Enlargements Of Filtrations written by Libo Li and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Business mathematics categories.
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.
Dynamic Markov Bridges And Market Microstructure
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Author : Umut Çetin
language : en
Publisher: Springer
Release Date : 2018-10-25
Dynamic Markov Bridges And Market Microstructure written by Umut Çetin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-25 with Mathematics categories.
This book undertakes a detailed construction of Dynamic Markov Bridges using a combination of theory and real-world applications to drive home important concepts and methodologies. In Part I, theory is developed using tools from stochastic filtering, partial differential equations, Markov processes, and their interplay. Part II is devoted to the applications of the theory developed in Part I to asymmetric information models among financial agents, which include a strategic risk-neutral insider who possesses a private signal concerning the future value of the traded asset, non-strategic noise traders, and competitive risk-neutral market makers. A thorough analysis of optimality conditions for risk-neutral insiders is provided and the implications on equilibrium of non-Gaussian extensions are discussed. A Markov bridge, first considered by Paul Lévy in the context of Brownian motion, is a mathematical system that undergoes changes in value from one state to another when the initial and final states are fixed. Markov bridges have many applications as stochastic models of real-world processes, especially within the areas of Economics and Finance. The construction of a Dynamic Markov Bridge, a useful extension of Markov bridge theory, addresses several important questions concerning how financial markets function, among them: how the presence of an insider trader impacts market efficiency; how insider trading on financial markets can be detected; how information assimilates in market prices; and the optimal pricing policy of a particular market maker. Principles in this book will appeal to probabilists, statisticians, economists, researchers, and graduate students interested in Markov bridges and market microstructure theory.
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
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.