Recent Advances In Stochastic Calculus

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Brownian Motion and Stochastic Calculus

Author : Ioannis Karatzas
Publisher : Springer
ISBN 13 : 1461209498
Total Pages : 490 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Brownian Motion and Stochastic Calculus by : Ioannis Karatzas

Download or read book Brownian Motion and Stochastic Calculus written by Ioannis Karatzas and published by Springer. This book was released on 2014-03-27 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graduate-course text, written for readers familiar with measure-theoretic probability and discrete-time processes, wishing 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, illustrated by results concerning representations of martingales and change of measure on Wiener space, which in turn permit a presentation of recent advances in financial economics. The 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 whole is backed by a large number of problems and exercises.

Stochastic Processes and Functional Analysis

Author : Alan C. Krinik
Publisher : CRC Press
ISBN 13 : 9780203913574
Total Pages : 526 pages
Book Rating : 4.9/5 (135 download)

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Book Synopsis Stochastic Processes and Functional Analysis by : Alan C. Krinik

Download or read book Stochastic Processes and Functional Analysis written by Alan C. Krinik and published by CRC Press. This book was released on 2004-03-23 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: This extraordinary compilation is an expansion of the recent American Mathematical Society Special Session celebrating M. M. Rao's distinguished career and includes most of the presented papers as well as ancillary contributions from session invitees. This book shows the effectiveness of abstract analysis for solving fundamental problems of stochas

Stochastic Calculus and Financial Applications

Author : J. Michael Steele
Publisher : Springer Science & Business Media
ISBN 13 : 1468493051
Total Pages : 303 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Stochastic Calculus and Financial Applications by : J. Michael Steele

Download or read book Stochastic Calculus and Financial Applications written by J. Michael Steele and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic calculus has important applications to mathematical finance. This book will appeal to practitioners and students who want an elementary introduction to these areas. From the reviews: "As the preface says, ‘This is a text with an attitude, and it is designed to reflect, wherever possible and appropriate, a prejudice for the concrete over the abstract’. This is also reflected in the style of writing which is unusually lively for a mathematics book." --ZENTRALBLATT MATH

Elementary Stochastic Calculus with Finance in View

Author : Thomas Mikosch
Publisher : World Scientific
ISBN 13 : 9789810235437
Total Pages : 230 pages
Book Rating : 4.2/5 (354 download)

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Book Synopsis Elementary Stochastic Calculus with Finance in View by : Thomas Mikosch

Download or read book Elementary Stochastic Calculus with Finance in View written by Thomas Mikosch and published by World Scientific. This book was released on 1998 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modelling with the Ito integral or stochastic differential equations has become increasingly important in various applied fields, including physics, biology, chemistry and finance. However, stochastic calculus is based on a deep mathematical theory. This book is suitable for the reader without a deep mathematical background. It gives an elementary introduction to that area of probability theory, without burdening the reader with a great deal of measure theory. Applications are taken from stochastic finance. In particular, the Black -- Scholes option pricing formula is derived. The book can serve as a text for a course on stochastic calculus for non-mathematicians or as elementary reading material for anyone who wants to learn about Ito calculus and/or stochastic finance.

Introduction to Stochastic Calculus with Applications

Author : Fima C. Klebaner
Publisher : Imperial College Press
ISBN 13 : 1860945554
Total Pages : 431 pages
Book Rating : 4.8/5 (69 download)

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Book Synopsis Introduction to Stochastic Calculus with Applications by : Fima C. Klebaner

Download or read book Introduction to Stochastic Calculus with Applications written by Fima C. Klebaner and published by Imperial College Press. This book was released on 2005 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a concise treatment of stochastic calculus and its applications. It gives a simple but rigorous treatment of the subject including a range of advanced topics, it is useful for practitioners who use advanced theoretical results. It covers advanced applications, such as models in mathematical finance, biology and engineering.Self-contained and unified in presentation, the book contains many solved examples and exercises. It may be used as a textbook by advanced undergraduates and graduate students in stochastic calculus and financial mathematics. It is also suitable for practitioners who wish to gain an understanding or working knowledge of the subject. For mathematicians, this book could be a first text on stochastic calculus; it is good companion to more advanced texts by a way of examples and exercises. For people from other fields, it provides a way to gain a working knowledge of stochastic calculus. It shows all readers the applications of stochastic calculus methods and takes readers to the technical level required in research and sophisticated modelling.This second edition contains a new chapter on bonds, interest rates and their options. New materials include more worked out examples in all chapters, best estimators, more results on change of time, change of measure, random measures, new results on exotic options, FX options, stochastic and implied volatility, models of the age-dependent branching process and the stochastic Lotka-Volterra model in biology, non-linear filtering in engineering and five new figures.Instructors can obtain slides of the text from the author.

Recent Advances in Stochastic Calculus

Author : John S. Baras
Publisher :
ISBN 13 :
Total Pages : 240 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Recent Advances in Stochastic Calculus by : John S. Baras

Download or read book Recent Advances in Stochastic Calculus written by John S. Baras and published by . This book was released on 1990 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Recent Development In Stochastic Dynamics And Stochastic Analysis

Author : Jinqiao Duan
Publisher : World Scientific
ISBN 13 : 981446760X
Total Pages : 306 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Recent Development In Stochastic Dynamics And Stochastic Analysis by : Jinqiao Duan

Download or read book Recent Development In Stochastic Dynamics And Stochastic Analysis written by Jinqiao Duan and published by World Scientific. This book was released on 2010-02-08 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic dynamical systems and stochastic analysis are of great interests not only to mathematicians but also to scientists in other areas. Stochastic dynamical systems tools for modeling and simulation are highly demanded in investigating complex phenomena in, for example, environmental and geophysical sciences, materials science, life sciences, physical and chemical sciences, finance and economics.The volume reflects an essentially timely and interesting subject and offers reviews on the recent and new developments in stochastic dynamics and stochastic analysis, and also some possible future research directions. Presenting a dozen chapters of survey papers and research by leading experts in the subject, the volume is written with a wide audience in mind ranging from graduate students, junior researchers to professionals of other specializations who are interested in the subject.

Lévy Processes and Stochastic Calculus

Author : David Applebaum
Publisher : Cambridge University Press
ISBN 13 : 1139477986
Total Pages : 461 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Lévy Processes and Stochastic Calculus by : David Applebaum

Download or read book Lévy Processes and Stochastic Calculus written by David Applebaum and published by Cambridge University Press. This book was released on 2009-04-30 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lévy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random noise. Here, the author ties these two subjects together, beginning with an introduction to the general theory of Lévy processes, then leading on to develop the stochastic calculus for Lévy processes in a direct and accessible way. This fully revised edition now features a number of new topics. These include: regular variation and subexponential distributions; necessary and sufficient conditions for Lévy processes to have finite moments; characterisation of Lévy processes with finite variation; Kunita's estimates for moments of Lévy type stochastic integrals; new proofs of Ito representation and martingale representation theorems for general Lévy processes; multiple Wiener-Lévy integrals and chaos decomposition; an introduction to Malliavin calculus; an introduction to stability theory for Lévy-driven SDEs.

Brownian Motion, Martingales, and Stochastic Calculus

Author : Jean-François Le Gall
Publisher : Springer
ISBN 13 : 3319310895
Total Pages : 282 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Brownian Motion, Martingales, and Stochastic Calculus by : Jean-François Le Gall

Download or read book Brownian Motion, Martingales, and Stochastic Calculus written by Jean-François Le Gall and published by Springer. This book was released on 2016-04-28 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested in such developments. Beginning graduate or advanced undergraduate students will benefit from this detailed approach to an essential area of probability theory. The emphasis is on concise and efficient presentation, without any concession to mathematical rigor. The material has been taught by the author for several years in graduate courses at two of the most prestigious French universities. The fact that proofs are given with full details makes the book particularly suitable for self-study. The numerous exercises help the reader to get acquainted with the tools of stochastic calculus.

Stochastic Processes, Finance And Control: A Festschrift In Honor Of Robert J Elliott

Author : Samuel N Cohen
Publisher : World Scientific
ISBN 13 : 9814483915
Total Pages : 605 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Stochastic Processes, Finance And Control: A Festschrift In Honor Of Robert J Elliott by : Samuel N Cohen

Download or read book Stochastic Processes, Finance And Control: A Festschrift In Honor Of Robert J Elliott written by Samuel N Cohen and published by World Scientific. This book was released on 2012-08-10 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of a series of new, peer-reviewed papers in stochastic processes, analysis, filtering and control, with particular emphasis on mathematical finance, actuarial science and engineering. Paper contributors include colleagues, collaborators and former students of Robert Elliott, many of whom are world-leading experts and have made fundamental and significant contributions to these areas.This book provides new important insights and results by eminent researchers in the considered areas, which will be of interest to researchers and practitioners. The topics considered will be diverse in applications, and will provide contemporary approaches to the problems considered. The areas considered are rapidly evolving. This volume will contribute to their development, and present the current state-of-the-art stochastic processes, analysis, filtering and control.Contributing authors include: H Albrecher, T Bielecki, F Dufour, M Jeanblanc, I Karatzas, H-H Kuo, A Melnikov, E Platen, G Yin, Q Zhang, C Chiarella, W Fleming, D Madan, R Mamon, J Yan, V Krishnamurthy.

Stochastic Calculus

Author : Paolo Baldi
Publisher : Springer
ISBN 13 : 3319622269
Total Pages : 632 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Stochastic Calculus by : Paolo Baldi

Download or read book Stochastic Calculus written by Paolo Baldi and published by Springer. This book was released on 2017-11-09 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to the theory of stochastic calculus and some of its applications. It is the only textbook on the subject to include more than two hundred exercises with complete solutions. After explaining the basic elements of probability, the author introduces more advanced topics such as Brownian motion, martingales and Markov processes. The core of the book covers stochastic calculus, including stochastic differential equations, the relationship to partial differential equations, numerical methods and simulation, as well as applications of stochastic processes to finance. The final chapter provides detailed solutions to all exercises, in some cases presenting various solution techniques together with a discussion of advantages and drawbacks of the methods used. Stochastic Calculus will be particularly useful to advanced undergraduate and graduate students wishing to acquire a solid understanding of the subject through the theory and exercises. Including full mathematical statements and rigorous proofs, this book is completely self-contained and suitable for lecture courses as well as self-study.

Brownian Motion

Author : René L. Schilling
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110307308
Total Pages : 424 pages
Book Rating : 4.1/5 (13 download)

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Book Synopsis Brownian Motion by : René L. Schilling

Download or read book Brownian Motion written by René L. Schilling and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-06-18 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Brownian motion is one of the most important stochastic processes in continuous time and with continuous state space. Within the realm of stochastic processes, Brownian motion is at the intersection of Gaussian processes, martingales, Markov processes, diffusions and random fractals, and it has influenced the study of these topics. Its central position within mathematics is matched by numerous applications in science, engineering and mathematical finance. Often textbooks on probability theory cover, if at all, Brownian motion only briefly. On the other hand, there is a considerable gap to more specialized texts on Brownian motion which is not so easy to overcome for the novice. The authors’ aim was to write a book which can be used as an introduction to Brownian motion and stochastic calculus, and as a first course in continuous-time and continuous-state Markov processes. They also wanted to have a text which would be both a readily accessible mathematical back-up for contemporary applications (such as mathematical finance) and a foundation to get easy access to advanced monographs. This textbook, tailored to the needs of graduate and advanced undergraduate students, covers Brownian motion, starting from its elementary properties, certain distributional aspects, path properties, and leading to stochastic calculus based on Brownian motion. It also includes numerical recipes for the simulation of Brownian motion.

Financial Calculus

Author : Martin Baxter
Publisher : Cambridge University Press
ISBN 13 : 9780521552899
Total Pages : 252 pages
Book Rating : 4.5/5 (528 download)

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Book Synopsis Financial Calculus by : Martin Baxter

Download or read book Financial Calculus written by Martin Baxter and published by Cambridge University Press. This book was released on 1996-09-19 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous introduction to the mathematics of pricing, construction and hedging of derivative securities.

Stochastic Calculus of Variations

Author : Yasushi Ishikawa
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110392321
Total Pages : 362 pages
Book Rating : 4.1/5 (13 download)

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Book Synopsis Stochastic Calculus of Variations by : Yasushi Ishikawa

Download or read book Stochastic Calculus of Variations written by Yasushi Ishikawa and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-03-07 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a concise introduction to the stochastic calculus of variations (also known as Malliavin calculus) for processes with jumps. It is written for researchers and graduate students who are interested in Malliavin calculus for jump processes. In this book "processes with jumps" includes both pure jump processes and jump-diffusions. The author provides many results on this topic in a self-contained way; this also applies to stochastic differential equations (SDEs) "with jumps". The book also contains some applications of the stochastic calculus for processes with jumps to the control theory and mathematical finance. Namely, asymptotic expansions functionals related with financial assets of jump-diffusion are provided based on the theory of asymptotic expansion on the Wiener–Poisson space. Solving the Hamilton–Jacobi–Bellman (HJB) equation of integro-differential type is related with solving the classical Merton problem and the Ramsey theory. The field of jump processes is nowadays quite wide-ranging, from the Lévy processes to SDEs with jumps. Recent developments in stochastic analysis have enabled us to express various results in a compact form. Up to now, these topics were rarely discussed in a monograph. Contents: Preface Preface to the second edition Introduction Lévy processes and Itô calculus Perturbations and properties of the probability law Analysis of Wiener–Poisson functionals Applications Appendix Bibliography List of symbols Index

Applied Stochastic Control of Jump Diffusions

Author : Bernt Øksendal
Publisher : Springer Science & Business Media
ISBN 13 : 3540698264
Total Pages : 263 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Applied Stochastic Control of Jump Diffusions by : Bernt Øksendal

Download or read book Applied Stochastic Control of Jump Diffusions written by Bernt Øksendal and published by Springer Science & Business Media. This book was released on 2007-04-26 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is a rigorous introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications. Discussion includes the dynamic programming method and the maximum principle method, and their relationship. The text emphasises real-world applications, primarily in finance. Results are illustrated by examples, with end-of-chapter exercises including complete solutions. The 2nd edition adds a chapter on optimal control of stochastic partial differential equations driven by Lévy processes, and a new section on optimal stopping with delayed information. Basic knowledge of stochastic analysis, measure theory and partial differential equations is assumed.

Stochastic Calculus and Applications

Author : Samuel N. Cohen
Publisher : Birkhäuser
ISBN 13 : 1493928678
Total Pages : 673 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Stochastic Calculus and Applications by : Samuel N. Cohen

Download or read book Stochastic Calculus and Applications written by Samuel N. Cohen and published by Birkhäuser. This book was released on 2015-11-18 with total page 673 pages. Available in PDF, EPUB and Kindle. Book excerpt: Completely revised and greatly expanded, the new edition of this text takes readers who have been exposed to only basic courses in analysis through the modern general theory of random processes and stochastic integrals as used by systems theorists, electronic engineers and, more recently, those working in quantitative and mathematical finance. Building upon the original release of this title, this text will be of great interest to research mathematicians and graduate students working in those fields, as well as quants in the finance industry. New features of this edition include: End of chapter exercises; New chapters on basic measure theory and Backward SDEs; Reworked proofs, examples and explanatory material; Increased focus on motivating the mathematics; Extensive topical index. "Such a self-contained and complete exposition of stochastic calculus and applications fills an existing gap in the literature. The book can be recommended for first-year graduate studies. It will be useful for all who intend to work with stochastic calculus as well as with its applications."–Zentralblatt (from review of the First Edition)

Stochastic Calculus for Finance I

Author : Steven Shreve
Publisher : Springer Science & Business Media
ISBN 13 : 9780387249681
Total Pages : 212 pages
Book Rating : 4.2/5 (496 download)

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Book Synopsis Stochastic Calculus for Finance I by : Steven Shreve

Download or read book Stochastic Calculus for Finance I written by Steven Shreve and published by Springer Science & Business Media. This book was released on 2005-06-28 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developed for the professional Master's program in Computational Finance at Carnegie Mellon, the leading financial engineering program in the U.S. Has been tested in the classroom and revised over a period of several years Exercises conclude every chapter; some of these extend the theory while others are drawn from practical problems in quantitative finance