From 26“30 September 2004, the “International Conference on Stochastic Finance 2004” took place at INSTITUTO SUPERIOR DE ECONOMIA E GEST/lo (
ISEG) da Universidade Técnica de Lisboa, in Portugal. The conference was one
of the ...

Author: Albert N. Shiryaev

Publisher: Springer Science & Business Media

ISBN: 9780387283593

Category: Mathematics

Page: 364

View: 751

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.

These include courses for a whole semester on Mathematical Finance in Berlin
and also short courses on special topics such as risk measures given at the
Institut Henri Poincaré in Paris, at the Department of Operations Research at
Cornell ...

Author: Hans Föllmer

Publisher: Walter de Gruyter

ISBN: 9783110218046

Category: Business & Economics

Page: 544

View: 996

This is the third, revised and extended edition of the classical introduction to the mathematics of finance, based on stochastic models in discrete time. In the first part of the book simple one-period models are studied, in the second part the idea of dynamic hedging of contingent claims is developed in a multiperiod framework. Due to the strong appeal and wide use of this book, it is now available as a textbook with exercises. It will be of value for a broad community of students and researchers. It may serve as basis for graduate courses and be also interesting for those who work in the financial industry and want to get an idea about the mathematical methods of risk assessment.

CHAPMAN & HALL/CRC Financial Mathematics Series Aims and scope: The
field of financial mathematics forms an ever-expanding slice of the financial
sector. This series aims to capture new developments and summarize what is
known ...

Author: Jan Vecer

Publisher: CRC Press

ISBN: 9781439812525

Category: Business & Economics

Page: 342

View: 190

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

Financial Mathematics Series Aims and scope: The field of financial mathematics
forms an ever-expanding slice of the financial sector. This series aims to capture
new developments and summarize what is known over the whole spectrum of ...

Author: Nicolas Privault

Publisher: CRC Press

ISBN: 9781466594036

Category: Business & Economics

Page: 441

View: 254

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

finance pays back enormously; (b) emphasize the clarity of exposition on the
generality of results and techniques in order ... any additional mathematical
complexity; (0) provide a pedagogical exposition of stochastic finance
methodologies that ...

Author: P. C. G. Vassiliou

Publisher: John Wiley & Sons

ISBN: 9781118618660

Category: Mathematics

Page: 416

View: 322

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.

At that time , staff members of economics and mathematics departments already
discussed the use of the Black and Scholes option pricing formula ; courses on stochastic finance were offered at leading institutions such as ETH Zürich ...

Author: Thomas Mikosch

Publisher: World Scientific

ISBN: 9810235437

Category: Mathematics

Page: 212

View: 260

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.

Apart from the intrinsic interest of presenting the material on mathematical finance, a major pedagogical motivation for introducing the courses was to
stimulate students to learn more about probability, martingales and stochastic
integration by ...

Author: Douglas Kennedy

Publisher: CRC Press

ISBN: 9781439882719

Category: Mathematics

Page: 264

View: 290

Filling the void between surveys of the field with relatively light mathematical content and books with a rigorous, formal approach to stochastic integration and probabilistic ideas, Stochastic Financial Models provides a sound introduction to mathematical finance. The author takes a classical applied mathematical approach, focusing on calculations rather than seeking the greatest generality. Developed from the esteemed author’s advanced undergraduate and graduate courses at the University of Cambridge, the text begins with the classical topics of utility and the mean-variance approach to portfolio choice. The remainder of the book deals with derivative pricing. The author fully explains the binomial model since it is central to understanding the pricing of derivatives by self-financing hedging portfolios. He then discusses the general discrete-time model, Brownian motion and the Black–Scholes model. The book concludes with a look at various interest-rate models. Concepts from measure-theoretic probability and solutions to the end-of-chapter exercises are provided in the appendices. By exploring the important and exciting application area of mathematical finance, this text encourages students to learn more about probability, martingales and stochastic integration. It shows how mathematical concepts, such as the Black–Scholes and Gaussian random-field models, are used in financial situations.

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: 590

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.

Author: Songsak SriboonchitaPublish On: 2009-10-19

Stieltjes measure and integrals cannot handle irregular observations in stochastic finance and hence we need another type of integral, namely the Ito
integral. When observation processes go beyond semimartingales, we need
some new ...

Author: Songsak Sriboonchita

Publisher: CRC Press

ISBN: 1420082671

Category: Business & Economics

Page: 455

View: 769

Drawing from many sources in the literature, Stochastic Dominance and Applications to Finance, Risk and Economics illustrates how stochastic dominance (SD) can be used as a method for risk assessment in decision making. It provides basic background on SD for various areas of applications. Useful Concepts and Techniques for Economics ApplicationsThe

This book gives an introduction to the theory of mathematical finance, which is
the modern approach to analyse options and derivatives. Roughly speaking, we
can divide mathematical finance into three main directions. In stochastic finance ...

Author: Fred Espen Benth

Publisher: Springer Science & Business Media

ISBN: 9783642187865

Category: Business & Economics

Page: 162

View: 765

This is a very basic and accessible introduction to option pricing, invoking a minimum of stochastic analysis and requiring only basic mathematical skills. It covers the theory essential to the statistical modeling of stocks, pricing of derivatives with martingale theory, and computational finance including both finite-difference and Monte Carlo methods.

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

variables as well as discrete-time finite-state stochastic processes that will be
introduced later. In Figure 2.1., we show how the information structures in
Example 2.2 is expressed in terms of an information tree. {85} {85,95} {95} {85,
95,105,115} ...

Author: X. Sheldon Lin

Publisher: John Wiley & Sons

ISBN: 9780471793205

Category: Mathematics

Page: 224

View: 930

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.

... Italy, July 6-12, 2003 CIME-EMS Summer School, Professor of Finance and
Howard J Creekmore Profe Kerry Back, Tomasz R. Bielecki, CIME-EMS School
on Stochastic Methods, Christian Hipp, Shige Peng, Walter Schachermayer.

However, the fact that the process BH is not a semimartingale, makes it difficult to
use fBm as the source of randomness in Stochastic Finance at least theoretically:
the reason is the fact that in the pricing models based on geometric fBm one ...

Author: Freddy Delbaen

Publisher: Springer Science & Business Media

ISBN: 9783642026089

Category: Mathematics

Page: 266

View: 117

Problems of stochastic optimization and various mathematical aspects of risk are the main themes of this contributed volume. The readers learn about the recent results and techniques of optimal investment, risk measures and derivative pricing. There are also papers touching upon credit risk, martingale theory and limit theorems. Forefront researchers in probability and financial mathematics have contributed to this volume paying tribute to Yuri Kabanov, an eminent researcher in probability and mathematical finance, on the occasion of his 60th birthday. The volume gives a fair overview of these topics and the current approaches.

In this thesis, stochastic volatility models are introduced and analysed with
special regard to the numerical problems ... of the two-dimensional system of stochastic differential equations required to price non-vanilla financial derivatives
.

Author: Christian Kahl

Publisher: Universal-Publishers

ISBN: 9781581123838

Category: Business & Economics

Page: 220

View: 989

The famous Black-Scholes model was the starting point of a new financial industry and has been a very important pillar of all options trading since. One of its core assumptions is that the volatility of the underlying asset is constant. It was realised early that one has to specify a dynamic on the volatility itself to get closer to market behaviour. There are mainly two aspects making this fact apparent. Considering historical evolution of volatility by analysing time series data one observes erratic behaviour over time. Secondly, backing out implied volatility from daily traded plain vanilla options, the volatility changes with strike. The most common realisations of this phenomenon are the implied volatility smile or skew. The natural question arises how to extend the Black-Scholes model appropriately. Within this book the concept of stochastic volatility is analysed and discussed with special regard to the numerical problems occurring either in calibrating the model to the market implied volatility surface or in the numerical simulation of the two-dimensional system of stochastic differential equations required to price non-vanilla financial derivatives. We introduce a new stochastic volatility model, the so-called Hyp-Hyp model, and use Watanabe's calculus to find an analytical approximation to the model implied volatility. Further, the class of affine diffusion models, such as Heston, is analysed in view of using the characteristic function and Fourier inversion techniques to value European derivatives.

This book introduces the theory of stochastic processes with applications taken from physics and finance.

Author: Wolfgang Paul

Publisher: Springer Science & Business Media

ISBN: 9783319003276

Category: Science

Page: 280

View: 187

This book introduces the theory of stochastic processes with applications taken from physics and finance. Fundamental concepts like the random walk or Brownian motion but also Levy-stable distributions are discussed. Applications are selected to show the interdisciplinary character of the concepts and methods. In the second edition of the book a discussion of extreme events ranging from their mathematical definition to their importance for financial crashes was included. The exposition of basic notions of probability theory and the Brownian motion problem as well as the relation between conservative diffusion processes and quantum mechanics is expanded. The second edition also enlarges the treatment of financial markets. Beyond a presentation of geometric Brownian motion and the Black-Scholes approach to option pricing as well as the econophysics analysis of the stylized facts of financial markets, an introduction to agent based modeling approaches is given.