Stochastic Calculus and Financial Applications

Author: J. Michael Steele
Publisher: Springer Science & Business Media
ISBN: 1468493051
Format: PDF, Mobi
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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: 9789810235437
Format: PDF
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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: World Scientific Publishing Company
ISBN: 1911298674
Format: PDF, Kindle
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This book presents a concise and rigorous treatment of stochastic calculus. It also gives its main applications in finance, biology and engineering. In finance, the stochastic calculus is applied to pricing options by no arbitrage. In biology, it is applied to populations' models, and in engineering it is applied to filter signal from noise. Not everything is proved, but enough proofs are given to make it a mathematically rigorous exposition. This book aims to present the theory of stochastic calculus and its applications to an audience which possesses only a basic knowledge of calculus and probability. It may be used as a textbook by graduate and advanced undergraduate students in stochastic processes, financial mathematics and engineering. It is also suitable for researchers to gain working knowledge of the subject. It contains many solved examples and exercises making it suitable for self study. In the book many of the concepts are introduced through worked-out examples, eventually leading to a complete, rigorous statement of the general result, and either a complete proof, a partial proof or a reference. Using such structure, the text will provide a mathematically literate reader with rapid introduction to the subject and its advanced applications. The book covers models in mathematical finance, biology and engineering. For mathematicians, this book can be used as a first text on stochastic calculus or as a companion to more rigorous texts by a way of examples and exercises. Contents:Preliminaries From CalculusConcepts of Probability TheoryBasic Stochastic ProcessesBrownian Motion CalculusStochastic Differential EquationsDiffusion ProcessesMartingalesCalculus for SemimartingalesPure Jump ProcessesChange of Probability MeasureApplications in Finance: Stock and FX OptionsApplications in Finance: Bonds, Rates and OptionsApplications in BiologyApplications in Engineering and Physics Readership: Academics, mathematicians, advanced undergraduates, graduates, practitioners in finance, risk managers and electrical engineers.

Stochastic Calculus for Quantitative Finance

Author: Alexander A Gushchin
Publisher: Elsevier
ISBN: 0081004761
Format: PDF, ePub, Docs
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In 1994 and 1998 F. Delbaen and W. Schachermayer published two breakthrough papers where they proved continuous-time versions of the Fundamental Theorem of Asset Pricing. This is one of the most remarkable achievements in modern Mathematical Finance which led to intensive investigations in many applications of the arbitrage theory on a mathematically rigorous basis of stochastic calculus. Mathematical Basis for Finance: Stochastic Calculus for Finance provides detailed knowledge of all necessary attributes in stochastic calculus that are required for applications of the theory of stochastic integration in Mathematical Finance, in particular, the arbitrage theory. The exposition follows the traditions of the Strasbourg school. This book covers the general theory of stochastic processes, local martingales and processes of bounded variation, the theory of stochastic integration, definition and properties of the stochastic exponential; a part of the theory of Lévy processes. Finally, the reader gets acquainted with some facts concerning stochastic differential equations. Contains the most popular applications of the theory of stochastic integration Details necessary facts from probability and analysis which are not included in many standard university courses such as theorems on monotone classes and uniform integrability Written by experts in the field of modern mathematical finance

A Modern Theory of Random Variation

Author: Patrick Muldowney
Publisher: John Wiley & Sons
ISBN: 1118345940
Format: PDF, Mobi
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A ground-breaking and practical treatment of probability and stochastic processes A Modern Theory of Random Variation is a new and radical re-formulation of the mathematical underpinnings of subjects as diverse as investment, communication engineering, and quantum mechanics. Setting aside the classical theory of probability measure spaces, the book utilizes a mathematically rigorous version of the theory of random variation that bases itself exclusively on finitely additive probability distribution functions. In place of twentieth century Lebesgue integration and measure theory, the author uses the simpler concept of Riemann sums, and the non-absolute Riemann-type integration of Henstock. Readers are supplied with an accessible approach to standard elements of probability theory such as the central limmit theorem and Brownian motion as well as remarkable, new results on Feynman diagrams and stochastic integrals. Throughout the book, detailed numerical demonstrations accompany the discussions of abstract mathematical theory, from the simplest elements of the subject to the most complex. In addition, an array of numerical examples and vivid illustrations showcase how the presented methods and applications can be undertaken at various levels of complexity. A Modern Theory of Random Variation is a suitable book for courses on mathematical analysis, probability theory, and mathematical finance at the upper-undergraduate and graduate levels. The book is also an indispensible resource for researchers and practitioners who are seeking new concepts, techniques and methodologies in data analysis, numerical calculation, and financial asset valuation. Patrick Muldowney, PhD, served as lecturer at the Magee Business School of the UNiversity of Ulster for over twenty years. Dr. Muldowney has published extensively in his areas of research, including integration theory, financial mathematics, and random variation.

Stochastic Calculus and Applications

Author: Samuel Cohen
Publisher: Birkhäuser
ISBN: 1493928678
Format: PDF, Mobi
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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 Differential Equations

Author: Bernt Oksendal
Publisher: Springer Science & Business Media
ISBN: 3662130505
Format: PDF, Kindle
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These notes are based on a postgraduate course I gave on stochastic differential equations at Edinburgh University in the spring 1982. No previous knowledge about the subject was assumed, but the presen tation is based on some background in measure theory. There are several reasons why one should learn more about stochastic differential equations: They have a wide range of applica tions outside mathematics, there are many fruitful connections to other mathematical disciplines and the subject has a rapidly develop ing life of its own as a fascinating research field with many interesting unanswered questions. Unfortunately most of the literature about stochastic differential equations seems to place so much emphasis on rigor and complete ness that is scares many nonexperts away. These notes are an attempt to approach the subject from the nonexpert point of view: Not knowing anything (except rumours, maybe) about a subject to start with, what would I like to know first of all? My answer would be: 1) In what situations does the subject arise? 2) What are its essential features? 3) What are the applications and the connections to other fields? I would not be so interested in the proof of the most general case, but rather in an easier proof of a special case, which may give just as much of the basic idea in the argument. And I would be willing to believe some basic results without proof (at first stage, anyway) in order to have time for some more basic applications.

Continuous time Stochastic Control and Optimization with Financial Applications

Author: Huyên Pham
Publisher: Springer Science & Business Media
ISBN: 3540895000
Format: PDF, Kindle
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Stochastic optimization problems arise in decision-making problems under uncertainty, and find various applications in economics and finance. On the other hand, problems in finance have recently led to new developments in the theory of stochastic control. This volume provides a systematic treatment of stochastic optimization problems applied to finance by presenting the different existing methods: dynamic programming, viscosity solutions, backward stochastic differential equations, and martingale duality methods. The theory is discussed in the context of recent developments in this field, with complete and detailed proofs, and is illustrated by means of concrete examples from the world of finance: portfolio allocation, option hedging, real options, optimal investment, etc. This book is directed towards graduate students and researchers in mathematical finance, and will also benefit applied mathematicians interested in financial applications and practitioners wishing to know more about the use of stochastic optimization methods in finance.

Methods of Mathematical Finance

Author: Ioannis Karatzas
Publisher: Springer
ISBN: 1493968459
Format: PDF, Kindle
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This sequel to Brownian Motion and Stochastic Calculus by the same authors develops contingent claim pricing and optimal consumption/investment in both complete and incomplete markets, within the context of Brownian-motion-driven asset prices. The latter topic is extended to a study of equilibrium, providing conditions for 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 book. This book will 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. The chapters on contingent claim valuation present techniques of practical importance, especially for pricing exotic options.