Ioannis Karatzas – författare & böcker

Del 113 - Graduate Texts in Mathematics

Brownian Motion and Stochastic Calculus

Häftad, Engelska, 1991

543 kr

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This book is designed as a text for graduate courses in stochastic processes. It is written for readers familiar with measure-theoretic probability and discrete-time processes who wish to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed. The power of this calculus is illustrated by results concerning representations of martingales and change of measure on Wiener space, and these in turn permit a presentation of recent advances in financial economics (option pricing and consumption/investment optimization). This book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The text is complemented by a large number of problems and exercises.

Ioannis Karatzas, B.S. Rajput, M. S. Taqqu, Ioannis Karatzas, Balram Rajput, I. Karatzas, B S Rajput, M S Taqqu, Murad S Taqqu - Stochastic Processes and Related Topics, Inbunden

Stochastic Processes and Related Topics

In Memory of Stamatis Cambanis 1943-1995

AvIoannis Karatzas,B.S. Rajputm. fl.

Inbunden, Engelska, 1998

972 kr

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Concerned with stable processes and other infinitely divisible models this volume collates articles covering a range of related topics. Issues covered include: results in heavy-tailed processes, the central limit problem; comparison and deviation problems; and probability and distrbution inequalities. Also included in the text are articles on: Markovian property and extreme values; interacting particle approximation, communication networks; the Italian problem; and global dependancy measure and prediction.

Brownian Motion and Stochastic Calculus

AvSteven Shreve,Ioannis Karatzas

E-bok

PDF, Engelska, 2014

712 kr

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This book is designed as a text for graduate courses in stochastic processes. It is written for readers familiar with measure-theoretic probability and discrete-time processes who wish to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed. The power of this calculus is illustrated by results concerning representations of martingales and change of measure on Wiener space, and these in turn permit a presentation of recent advances in financial economics (option pricing and consumption/investment optimization).

This book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The text is complemented by a large number of problems and exercises.

Stochastic Processes and Related Topics

In Memory of Stamatis Cambanis 1943–1995

AvMurad S. Taqqu,Balram Rajputm. fl.

E-bok

PDF, Engelska, 2012

712 kr

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In the last twenty years extensive research has been devoted to a better understanding of the stable and other closely related infinitely divisible mod els. Stamatis Cambanis, a distinguished educator and researcher, played a special leadership role in the development of these research efforts, particu larly related to stable processes from the early seventies until his untimely death in April ''95. This commemorative volume consists of a collection of research articles devoted to reviewing the state of the art of this and other rapidly developing research and to explore new directions of research in these fields. The volume is a tribute to the Life and Work of Stamatis by his students, friends, and colleagues whose personal and professional lives he has deeply touched through his generous insights and dedication to his profession. Before the idea of this volume was conceived, two conferences were held in the memory of Stamatis. The first was organized by the University of Athens and the Athens University of Economics and was held in Athens during December 18-19, 1995. The second was a significant part of a Spe cial IMS meeting held at the campus of the University of North Carolina at Chapel Hill during October 17-19, 1996. It is the selfless effort of sev eral people that brought about these conferences. We believe that this is an appropriate place to acknowledge their effort; and on behalf of all the participants, we extend sincere thanks to all these persons.

Stochastic Processes and Related Topics

In Memory of Stamatis Cambanis 1943–1995

AvIoannis Karatzas,Balram Rajputm. fl.

Häftad, Engelska, 2012

543 kr

Skickas inom 10-15 vardagar

In the last twenty years extensive research has been devoted to a better understanding of the stable and other closely related infinitely divisible mod els. Stamatis Cambanis, a distinguished educator and researcher, played a special leadership role in the development of these research efforts, particu larly related to stable processes from the early seventies until his untimely death in April '95. This commemorative volume consists of a collection of research articles devoted to reviewing the state of the art of this and other rapidly developing research and to explore new directions of research in these fields. The volume is a tribute to the Life and Work of Stamatis by his students, friends, and colleagues whose personal and professional lives he has deeply touched through his generous insights and dedication to his profession. Before the idea of this volume was conceived, two conferences were held in the memory of Stamatis. The first was organized by the University of Athens and the Athens University of Economics and was held in Athens during December 18-19, 1995. The second was a significant part of a Spe cial IMS meeting held at the campus of the University of North Carolina at Chapel Hill during October 17-19, 1996. It is the selfless effort of sev eral people that brought about these conferences. We believe that this is an appropriate place to acknowledge their effort; and on behalf of all the participants, we extend sincere thanks to all these persons.

Brownian Motion and Stochastic Calculus

AvSteven Shreve,Ioannis Karatzas

E-bok

PDF, Engelska, 2012

1 140 kr

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Two of the most fundamental concepts in the theory of stochastic processes are the Markov property and the martingale property. * This book is written for readers who are acquainted with both of these ideas in the discrete-time setting, and who now wish to explore stochastic processes in their continuous time context. It has been our goal to write a systematic and thorough exposi tion of this subject, leading in many instances to the frontiers of knowledge. At the same time, we have endeavored to keep the mathematical prerequisites as low as possible, namely, knowledge of measure-theoretic probability and some familiarity with discrete-time processes. The vehicle we have chosen for this task is Brownian motion, which we present as the canonical example of both a Markov process and a martingale. We support this point of view by showing how, by means of stochastic integration and random time change, all continuous-path martingales and a multitude of continuous-path Markov processes can be represented in terms of Brownian motion. This approach forces us to leave aside those processes which do not have continuous paths. Thus, the Poisson process is not a primary object of study, although it is developed in Chapter 1 to be used as a tool when we later study passage times and local time of Brownian motion.

Portfolio Theory and Arbitrage

A Course in Mathematical Finance

AvIoannis Karatzas,Constantinos Kardaras

Häftad, Engelska, 2022

1 006 kr

Skickas inom 5-8 vardagar

This book develops a mathematical theory for finance, based on a simple and intuitive absence-of-arbitrage principle. This posits that it should not be possible to fund a non-trivial liability, starting with initial capital arbitrarily near zero. The principle is easy-to-test in specific models, as it is described in terms of the underlying market characteristics; it is shown to be equivalent to the existence of the so-called ""Kelly"" or growth-optimal portfolio, of the log-optimal portfolio, and of appropriate local martingale deflators. The resulting theory is powerful enough to treat in great generality the fundamental questions of hedging, valuation, and portfolio optimization.The book contains a considerable amount of new research and results, as well as a significant number of exercises. It can be used as a basic text for graduate courses in Probability and Stochastic Analysis, and in Mathematical Finance. No prior familiarity with finance is required, but it is assumed that readers have a good working knowledge of real analysis, measure theory, and of basic probability theory. Familiarity with stochastic analysis is also assumed, as is integration with respect to continuous semimartingales.

Del 39 - Probability Theory and Stochastic Modelling

Methods of Mathematical Finance

AvIoannis Karatzas,Steven Shreve

Inbunden, Engelska, 2016

1 508 kr

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This monograph is a sequel to Brownian Motion and Stochastic Calculus by the same authors. Within the context of Brownian-motion-driven asset prices, it develops contingent claim pricing and optimal consumption/investment in both complete and incomplete markets. The latter topic is extended to the study of complete market equilibrium, providing conditions for the existence and uniqueness of market prices which support trading by several heterogeneous agents. Although much of the incomplete-market material is available in research papers, these topics are treated for the first time in a unified manner. The book contains an extensive set of references and notes describing the field, including topics not treated in the text. This monograph should be of interest to researchers wishing to see advanced mathematics applied to finance. The material on optimal consumption and investment, leading to equilibrium, is addressed to the theoretical finance community. Thechapters on contingent claim valuation present techniques of practical importance, especially for pricing exotic options.The present corrected printing includes, besides other minor corrections, an important correction of Theorem 6.4 and a simplification of the proof of Lemma 6.5. Also available by Ioannis Karatzas and Steven E. Shreve, Brownian Motion and Stochastic Calculus, Second Edition, Springer-Verlag New York, Inc., 1991, 470 pp., ISBN 0-387- 97655-8.

Methods of Mathematical Finance

AvSteven Shreve,Ioannis Karatzas

E-bok

PDF, Engelska, 2017

1 891 kr

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This monograph is a sequel to Brownian Motion and Stochastic Calculus by the same authors. Within the context of Brownian-motion-driven asset prices, it develops contingent claim pricing and optimal consumption/investment in both complete and incomplete markets. The latter topic is extended to the study of complete market equilibrium, providing conditions for the existence and uniqueness of market prices which support trading by several heterogeneous agents. Although much of the incomplete-market material is available in research papers, these topics are treated for the first time in a unified manner. The book contains an extensive set of references and notes describing the field, including topics not treated in the text.

This monograph should be of interest to researchers wishing to see advanced mathematics applied to finance. The material on optimal consumption and investment, leading to equilibrium, is addressed to the theoretical finance community. Thechapters on contingent claim valuation present techniques of practical importance, especially for pricing exotic options.

The present corrected printing includes, besides other minor corrections, an important correction of Theorem 6.4 and a simplification of the proof of Lemma 6.5.

Also available by Ioannis Karatzas and Steven E. Shreve, Brownian Motion and Stochastic Calculus, Second Edition, Springer-Verlag New York, Inc., 1991, 470 pp., ISBN 0-387- 97655-8.

Del 177 - Lecture Notes in Control and Information Sciences

Applied Stochastic Analysis

Proceedings of a US-French Workshop, Rutgers University, New Brunswick, N.J., April 29 – May 2, 1991

AvIoannis Karatzas,Daniel Ocone

Häftad, Engelska, 1992

543 kr

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This volume contains papers presented during a four-dayWorkshop that took place at Rutgers University from 29 Aprilto 2 May, 1991. The purpose of this workshop was to promoteinteraction among specialists in these areas byprovidingfor all an up-to-date picture of current issues andoutstanding problems.The topics covered include singular stochasticcontrol,queuing networks, the mathematical theory of stochasticoptimization and filtering, adaptive control and theestimation for random fields and its connections withsimulated annealing, statistical mechanics, andcombinatorial optimization.

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Ioannis Karatzas – författare

Brownian Motion and Stochastic Calculus

Stochastic Processes and Related Topics

Brownian Motion and Stochastic Calculus

Stochastic Processes and Related Topics

Stochastic Processes and Related Topics

Brownian Motion and Stochastic Calculus

Portfolio Theory and Arbitrage

Methods of Mathematical Finance

Methods of Mathematical Finance

Applied Stochastic Analysis

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