This book gives a systematic introduction to the basic theory of financial mathematics, with an emphasis on applications of martingale methods in pricing and hedging of contingent claims, interest rate term structure models, and expected ...

Author: Jia-An Yan

Publisher: Springer

ISBN: 9789811316579

Category: Mathematics

Page: 403

View: 588

This book gives a systematic introduction to the basic theory of financial mathematics, with an emphasis on applications of martingale methods in pricing and hedging of contingent claims, interest rate term structure models, and expected utility maximization problems. The general theory of static risk measures, basic concepts and results on markets of semimartingale model, and a numeraire-free and original probability based framework for financial markets are also included. The basic theory of probability and Ito's theory of stochastic analysis, as preliminary knowledge, are presented.

This book is being published in two volumes. The first volume presents the binomial asset-pricing model primarily as a vehicle for introducing in the simple setting the concepts needed for the continuous-time theory in the second volume.

Author: Steven Shreve

Publisher: Springer Science & Business Media

ISBN: 0387249680

Category: Mathematics

Page: 187

View: 804

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

This book is an introduction to financial mathematics.

Author: Hans Föllmer

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 9783110463453

Category: Mathematics

Page: 608

View: 176

This book is an introduction to financial mathematics. It is intended for graduate students in mathematics and for researchers working in academia and industry. The focus on stochastic models in discrete time has two immediate benefits. First, the probabilistic machinery is simpler, and one can discuss right away some of the key problems in the theory of pricing and hedging of financial derivatives. Second, the paradigm of a complete financial market, where all derivatives admit a perfect hedge, becomes the exception rather than the rule. Thus, the need to confront the intrinsic risks arising from market incomleteness appears at a very early stage. The first part of the book contains a study of a simple one-period model, which also serves as a building block for later developments. Topics include the characterization of arbitrage-free markets, preferences on asset profiles, an introduction to equilibrium analysis, and monetary measures of financial risk. In the second part, the idea of dynamic hedging of contingent claims is developed in a multiperiod framework. Topics include martingale measures, pricing formulas for derivatives, American options, superhedging, and hedging strategies with minimal shortfall risk. This fourth, newly revised edition contains more than one hundred exercises. It also includes material on risk measures and the related issue of model uncertainty, in particular a chapter on dynamic risk measures and sections on robust utility maximization and on efficient hedging with convex risk measures. Contents: Part I: Mathematical finance in one period Arbitrage theory Preferences Optimality and equilibrium Monetary measures of risk Part II: Dynamic hedging Dynamic arbitrage theory American contingent claims Superhedging Efficient hedging Hedging under constraints Minimizing the hedging error Dynamic risk measures

International Journal of Theoretical and Applied Finance 4(1), 23–43. Hull, J. and A. White (1990). Pricing interest-rate-derivative securities. Review of Financial Studies 3(4), 573–592. Hull, J. C. (2008). ... Stochastic integral.

Author: Jan Vecer

Publisher: CRC Press

ISBN: 9781439812525

Category: Business & Economics

Page: 342

View: 378

Unlike much of the existing literature, Stochastic Finance: A Numeraire Approach treats price as a number of units of one asset needed for an acquisition of a unit of another asset instead of expressing prices in dollar terms exclusively. This numeraire approach leads to simpler pricing options for complex products, such as barrier, lookback, quant

Cambridge University Press, Cambridge, 538–574, 2001. Sekine, J., Dynamic minimization of worst conditional expectation of shortfall. Math. Finance. 14 (2004), 605–618. Shreve, S., Stochastic Calculus Models for Finance: Discrete Time.

Author: Hans Föllmer

Publisher: Walter de Gruyter

ISBN: 9783110218053

Category: Mathematics

Page: 555

View: 151

This book is an introduction to financial mathematics. It is intended for graduate students in mathematics and for researchers working in academia and industry. The focus on stochastic models in discrete time has two immediate benefits. First, the probabilistic machinery is simpler, and one can discuss right away some of the key problems in the theory of pricing and hedging of financial derivatives. Second, the paradigm of a complete financial market, where all derivatives admit a perfect hedge, becomes the exception rather than the rule. Thus, the need to confront the intrinsic risks arising from market incomleteness appears at a very early stage. The first part of the book contains a study of a simple one-period model, which also serves as a building block for later developments. Topics include the characterization of arbitrage-free markets, preferences on asset profiles, an introduction to equilibrium analysis, and monetary measures of financial risk. In the second part, the idea of dynamic hedging of contingent claims is developed in a multiperiod framework. Topics include martingale measures, pricing formulas for derivatives, American options, superhedging, and hedging strategies with minimal shortfall risk. This third revised and extended edition now contains more than one hundred exercises. It also includes new material on risk measures and the related issue of model uncertainty, in particular a new chapter on dynamic risk measures and new sections on robust utility maximization and on efficient hedging with convex risk measures.

From 26“30 September 2004, the “International Conference on Stochastic Finance 2004” took place at INSTITUTO SUPERIOR ... The conference was one of the biggest international forums for scientists and practitioners Working in financial ...

Author: Albert N. Shiryaev

Publisher: Springer Science & Business Media

ISBN: 9780387283593

Category: Mathematics

Page: 364

View: 369

Since the pioneering work of Black, Scholes, and Merton in the field of financial mathematics, research has led to the rapid development of a substantial body of knowledge, with plenty of applications to the common functioning of the world’s financial institutions. Mathematics, as the language of science, has always played a role in the development of knowledge and technology. Presently, the high-tech character of modern business has increased the need for advanced methods, which rely to a large extent on mathematical techniques. It has become essential for the financial analyst to possess a high degree of proficiency in these mathematical techniques.

2. lt"o Calculus. Cambridge University Press. Cambridge. Rolski, T., Schmidili, H., Schmidt, V., and Teugels, J. (1999). Stochastic Processes for Insurance and Finance. J. Wiley. Ross, SM. (1996). Stochastic Process. Second Edition.

Author: P. C. G. Vassiliou

Publisher: John Wiley & Sons

ISBN: 9781118618660

Category: Mathematics

Page: 416

View: 976

Stochastic finance and financial engineering have been rapidly expanding fields of science over the past four decades, mainly due to the success of sophisticated quantitative methodologies in helping professionals manage financial risks. In recent years, we have witnessed a tremendous acceleration in research efforts aimed at better comprehending, modeling and hedging this kind of risk. These two volumes aim to provide a foundation course on applied stochastic finance. They are designed for three groups of readers: firstly, students of various backgrounds seeking a core knowledge on the subject of stochastic finance; secondly financial analysts and practitioners in the investment, banking and insurance industries; and finally other professionals who are interested in learning advanced mathematical and stochastic methods, which are basic knowledge in many areas, through finance. Volume 1 starts with the introduction of the basic financial instruments and the fundamental principles of financial modeling and arbitrage valuation of derivatives. Next, we use the discrete-time binomial model to introduce all relevant concepts. The mathematical simplicity of the binomial model also provides us with the opportunity to introduce and discuss in depth concepts such as conditional expectations and martingales in discrete time. However, we do not expand beyond the needs of the stochastic finance framework. Numerous examples, each highlighted and isolated from the text for easy reference and identification, are included. The book concludes with the use of the binomial model to introduce interest rate models and the use of the Markov chain model to introduce credit risk. This volume is designed in such a way that, among other uses, makes it useful as an undergraduate course.

However, stochastic calculus is based on a deep mathematical theory. This book is suitable for the reader without a deep mathematical background.

Author: Thomas Mikosch

Publisher: World Scientific

ISBN: 9810235437

Category: Mathematics

Page: 212

View: 759

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.

Finance and Stochastics, 3(3):251 273, 1999. ISSN 0949-2984. ... Finance and Stochastics, 4(2):117 146, 2000. Hans Föllmer and Alexander Schied. Stochastic finance, volume 27 of de Gruyter Studies in Mathematics.

Author: Damien Lamberton

Publisher: CRC Press

ISBN: 9781420009941

Category: Business & Economics

Page: 254

View: 360

Since the publication of the first edition of this book, the area of mathematical finance has grown rapidly, with financial analysts using more sophisticated mathematical concepts, such as stochastic integration, to describe the behavior of markets and to derive computing methods. Maintaining the lucid style of its popular predecessor, Introduction

Introduction to Stochastic Calculus Applied to Finance D. LAMBERTON and B. LAPEYRE In recent years the growing importance of derivative products in financial markets has increased the demand for mathematical skills in financial ...

Author: Damien Lamberton

Publisher: CRC Press

ISBN: 0412718006

Category: Mathematics

Page: 200

View: 918

In recent years the growing importance of derivative products financial markets has increased financial institutions' demands for mathematical skills. This book introduces the mathematical methods of financial modeling with clear explanations of the most useful models. Introduction to Stochastic Calculus begins with an elementary presentation of discrete models, including the Cox-Ross-Rubenstein model. This book will be valued by derivatives trading, marketing, and research divisions of investment banks and other institutions, and also by graduate students and research academics in applied probability and finance theory.

Stochastic Finance: An Introduction with Market Examples presents an introduction to pricing and hedging in discrete and continuous time financial models without friction, emphasizing the complementarity of analytical and probabilistic ...

Author: Nicolas Privault

Publisher: CRC Press

ISBN: 9781466594036

Category: Business & Economics

Page: 441

View: 521

Stochastic Finance: An Introduction with Market Examples presents an introduction to pricing and hedging in discrete and continuous time financial models without friction, emphasizing the complementarity of analytical and probabilistic methods. It demonstrates both the power and limitations of mathematical models in finance, covering the basics of

This book is an introduction to financial mathematics. The first part of the book studies a simple one-period model which serves as a building block for later developments.

Author: Hans Föllmer

Publisher: Walter de Gruyter

ISBN: 9783110212075

Category: Mathematics

Page: 470

View: 267

This book is an introduction to financial mathematics. The first part of the book studies a simple one-period model which serves as a building block for later developments. Topics include the characterization of arbitrage-free markets, preferences on asset profiles, an introduction to equilibrium analysis, and monetary measures of risk. In the second part, the idea of dynamic hedging of contingent claims is developed in a multiperiod framework. Such models are typically incomplete: They involve intrinsic risks which cannot be hedged away completely. Topics include martingale measures, pricing formulas for derivatives, American options, superhedging, and hedging strategies with minimal shortfall risk. In addition to many corrections and improvements, this second edition contains several new sections, including a systematic discussion of law-invariant risk measures and of the connections between American options, superhedging, and dynamic risk measures.

As Volume II of the four-volume Problems and Solutions in Mathematical Finance series, this book provides clear explanation of the mathematics behind equity derivatives, in order to help readers gain a deeper understanding of their ...

Author: Eric Chin

Publisher: John Wiley & Sons

ISBN: 9781119966111

Category: Business & Economics

Page: 856

View: 603

Detailed guidance on the mathematics behind equity derivatives Problems and Solutions in Mathematical Finance Volume II is an innovative reference for quantitative practitioners and students, providing guidance through a range of mathematical problems encountered in the finance industry. This volume focuses solely on equity derivatives problems, beginning with basic problems in derivatives securities before moving on to more advanced applications, including the construction of volatility surfaces to price exotic options. By providing a methodology for solving theoretical and practical problems, whilst explaining the limitations of financial models, this book helps readers to develop the skills they need to advance their careers. The text covers a wide range of derivatives pricing, such as European, American, Asian, Barrier and other exotic options. Extensive appendices provide a summary of important formulae from calculus, theory of probability, and differential equations, for the convenience of readers. As Volume II of the four-volume Problems and Solutions in Mathematical Finance series, this book provides clear explanation of the mathematics behind equity derivatives, in order to help readers gain a deeper understanding of their mechanics and a firmer grasp of the calculations. Review the fundamentals of equity derivatives Work through problems from basic securities to advanced exotics pricing Examine numerical methods and detailed derivations of closed-form solutions Utilise formulae for probability, differential equations, and more Mathematical finance relies on mathematical models, numerical methods, computational algorithms and simulations to make trading, hedging, and investment decisions. For the practitioners and graduate students of quantitative finance, Problems and Solutions in Mathematical Finance Volume II provides essential guidance principally towards the subject of equity derivatives.

This book is an introduction to stochastic analysis and quantitative finance; it includes both theoretical and computational methods.

Author: Geon Ho Choe

Publisher: Springer

ISBN: 3319255878

Category: Mathematics

Page:

View: 899

This book is an introduction to stochastic analysis and quantitative finance; it includes both theoretical and computational methods. Topics covered are stochastic calculus, option pricing, optimal portfolio investment, and interest rate models. Also included are simulations of stochastic phenomena, numerical solutions of the Black–Scholes–Merton equation, Monte Carlo methods, and time series. Basic measure theory is used as a tool to describe probabilistic phenomena. The level of familiarity with computer programming is kept to a minimum. To make the book accessible to a wider audience, some background mathematical facts are included in the first part of the book and also in the appendices. This work attempts to bridge the gap between mathematics and finance by using diagrams, graphs and simulations in addition to rigorous theoretical exposition. Simulations are not only used as the computational method in quantitative finance, but they can also facilitate an intuitive and deeper understanding of theoretical concepts. Stochastic Analysis for Finance with Simulations is designed for readers who want to have a deeper understanding of the delicate theory of quantitative finance by doing computer simulations in addition to theoretical study. It will particularly appeal to advanced undergraduate and graduate students in mathematics and business, but not excluding practitioners in finance industry.

The MMF books start financially from scratch and mathematically assume only undergraduate calculus, linear algebra ... Ekkehard Kopp, Jan Malczak, Tomasz Zastawniak [SCF] Stochastic Calculus for Finance, Marek Capir'lski, Ekkehard Kopp, ...

Author: Marek Capiński

Publisher: Cambridge University Press

ISBN: 9781139560405

Category: Business & Economics

Page:

View: 841

This book focuses specifically on the key results in stochastic processes that have become essential for finance practitioners to understand. The authors study the Wiener process and Itô integrals in some detail, with a focus on results needed for the Black–Scholes option pricing model. After developing the required martingale properties of this process, the construction of the integral and the Itô formula (proved in detail) become the centrepiece, both for theory and applications, and to provide concrete examples of stochastic differential equations used in finance. Finally, proofs of the existence, uniqueness and the Markov property of solutions of (general) stochastic equations complete the book. Using careful exposition and detailed proofs, this book is a far more accessible introduction to Itô calculus than most texts. Students, practitioners and researchers will benefit from its rigorous, but unfussy, approach to technical issues. Solutions to the exercises are available online.

Author: Alexander A GushchinPublish On: 2015-08-26

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.

Author: Alexander A Gushchin

Publisher: Elsevier

ISBN: 9780081004760

Category: Mathematics

Page: 208

View: 261

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

stochastic processes and stochastic calculus in particular came in the late I960s and early 1970s when a series of seminal research papers in option pricing were published by Fisher Black, Robert Merton and Myron Scholes, among others.

Author: X. Sheldon Lin

Publisher: John Wiley & Sons

ISBN: 9780471793205

Category: Mathematics

Page: 224

View: 470

Incorporates the many tools needed for modeling and pricing infinance and insurance Introductory Stochastic Analysis for Finance and Insuranceintroduces readers to the topics needed to master and use basicstochastic analysis techniques for mathematical finance. The authorpresents the theories of stochastic processes and stochasticcalculus and provides the necessary tools for modeling and pricingin finance and insurance. Practical in focus, the book's emphasisis on application, intuition, and computation, rather thantheory. Consequently, the text is of interest to graduate students,researchers, and practitioners interested in these areas. While thetext is self-contained, an introductory course in probabilitytheory is beneficial to prospective readers. This book evolved from the author's experience as an instructor andhas been thoroughly classroom-tested. Following an introduction,the author sets forth the fundamental information and tools neededby researchers and practitioners working in the financial andinsurance industries: * Overview of Probability Theory * Discrete-Time stochastic processes * Continuous-time stochastic processes * Stochastic calculus: basic topics The final two chapters, Stochastic Calculus: Advanced Topics andApplications in Insurance, are devoted to more advanced topics.Readers learn the Feynman-Kac formula, the Girsanov's theorem, andcomplex barrier hitting times distributions. Finally, readersdiscover how stochastic analysis and principles are applied inpractice through two insurance examples: valuation of equity-linkedannuities under a stochastic interest rate environment andcalculation of reserves for universal life insurance. Throughout the text, figures and tables are used to help simplifycomplex theory and pro-cesses. An extensive bibliography opens upadditional avenues of research to specialized topics. Ideal for upper-level undergraduate and graduate students, thistext is recommended for one-semester courses in stochastic financeand calculus. It is also recommended as a study guide forprofessionals taking Causality Actuarial Society (CAS) and Societyof Actuaries (SOA) actuarial examinations.

This new book, demonstrating the relevance of Malliavin calculus for Mathematical Finance, starts with an exposition from scratch of this theory. Greeks (price sensitivities) are reinterpreted in terms of Malliavin calculus.

Author: Paul Malliavin

Publisher: Springer Science & Business Media

ISBN: 9783540307990

Category: Business & Economics

Page: 142

View: 836

Highly esteemed author Topics covered are relevant and timely

Stochastic calculus has important applications to mathematical finance. This book will appeal to practitioners and students who want an elementary introduction to these areas.

Author: J. Michael Steele

Publisher: Springer Science & Business Media

ISBN: 9781468493054

Category: Mathematics

Page: 302

View: 290

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