Download or read book Random Times and Enlargements of Filtrations in a Brownian Setting written by Roger Mansuy and published by Springer Science & Business Media. This book was released on 2006-02-10 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Enlargement of Filtration with Finance in View written by Anna Aksamit and published by Springer. This book was released on 2017-11-18 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Local Times and Excursion Theory for Brownian Motion written by Ju-Yi Yen and published by Springer. This book was released on 2013-10-01 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Option Prices as Probabilities written by Christophe Profeta and published by Springer Science & Business Media. This book was released on 2010-01-26 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 ? ?

Download or read book Penalising Brownian Paths written by Bernard Roynette and published by Springer. This book was released on 2009-07-31 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Aspects of Brownian Motion written by Roger Mansuy and published by Springer Science & Business Media. This book was released on 2008-09-16 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Dynamic Markov Bridges and Market Microstructure written by Umut Çetin and published by Springer. This book was released on 2018-10-25 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book S minaire de Probabilit s XLIV written by Catherine Donati-Martin and published by Springer. This book was released on 2012-05-12 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Contemporary Quantitative Finance written by Carl Chiarella and published by Springer Science & Business Media. This book was released on 2010-07-23 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Stochastic Calculus via Regularizations written by Francesco Russo and published by Springer Nature. This book was released on 2022-11-15 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Portfolio Optimization with Different Information Flow written by Caroline Hillairet and published by Elsevier. This book was released on 2017-02-10 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Counterexamples in Probability written by Jordan M. Stoyanov and published by Courier Corporation. This book was released on 2014-01-15 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: "While most mathematical examples illustrate the truth of a statement, counterexamples demonstrate a statement's falsity. Enjoyable topics of study, counterexamples are valuable tools for teaching and learning. The definitive book on the subject in regards to probability, this third edition features the author's revisions and corrections plus a substantial new appendix. 2013 edition"--

Download or read book Random Perturbation of PDEs and Fluid Dynamic Models written by Franco Flandoli and published by Springer. This book was released on 2011-03-02 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book deals with the random perturbation of PDEs which lack well-posedness, mainly because of their non-uniqueness, in some cases because of blow-up. The aim is to show that noise may restore uniqueness or prevent blow-up. This is not a general or easy-to-apply rule, and the theory presented in the book is in fact a series of examples with a few unifying ideas. The role of additive and bilinear multiplicative noise is described and a variety of examples are included, from abstract parabolic evolution equations with non-Lipschitz nonlinearities to particular fluid dynamic models, like the dyadic model, linear transport equations and motion of point vortices.

Download or read book Advanced Financial Modelling written by Hansjörg Albrecher and published by Walter de Gruyter. This book was released on 2009-12-15 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of state–of–the–art surveys on various topics in mathematical finance, with an emphasis on recent modelling and computational approaches. The volume is related to a 'Special Semester on Stochastics with Emphasis on Finance' that took place from September to December 2008 at the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences in Linz, Austria.

Download or read book S minaire de Probabilit s LI written by Catherine Donati-Martin and published by Springer Nature. This book was released on 2022-05-13 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a selection of texts that reflects the current research streams in probability, with an interest toward topics such as filtrations, Markov processes and Markov chains as well as large deviations, Stochastic Partial Differential equations, rough paths theory, quantum probabilities and percolation on graphs. The featured contributors are R. L. Karandikar and B. V. Rao, C. Leuridan, M. Vidmar, L. Miclo and P. Patie, A. Bernou, M.-E. Caballero and A. Rouault, J. Dedecker, F. Merlevède and E. Rio, F. Brosset, T. Klein, A. Lagnoux and P. Petit, C. Marinelli and L. Scarpa, C. Castaing, N. Marie and P. Raynaud de Fitte, S. Attal, J. Deschamps and C. Pellegrini, and N. Eisenbaum.

Download or read book Lebesgue and Sobolev Spaces with Variable Exponents written by Lars Diening and published by Springer Science & Business Media. This book was released on 2011-03-31 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of variable exponent function spaces has witnessed an explosive growth in recent years. The standard reference article for basic properties is already 20 years old. Thus this self-contained monograph collecting all the basic properties of variable exponent Lebesgue and Sobolev spaces is timely and provides a much-needed accessible reference work utilizing consistent notation and terminology. Many results are also provided with new and improved proofs. The book also presents a number of applications to PDE and fluid dynamics.

Download or read book Some Mathematical Models from Population Genetics written by Alison Etheridge and published by Springer Science & Business Media. This book was released on 2011-01-07 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work reflects sixteen hours of lectures delivered by the author at the 2009 St Flour summer school in probability. It provides a rapid introduction to a range of mathematical models that have their origins in theoretical population genetics. The models fall into two classes: forwards in time models for the evolution of frequencies of different genetic types in a population; and backwards in time (coalescent) models that trace out the genealogical relationships between individuals in a sample from the population. Some, like the classical Wright-Fisher model, date right back to the origins of the subject. Others, like the multiple merger coalescents or the spatial Lambda-Fleming-Viot process are much more recent. All share a rich mathematical structure. Biological terms are explained, the models are carefully motivated and tools for their study are presented systematically.