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Martingales and Financial Mathematics in Discrete Time

Author : Benoîte de Saporta

Publisher : John Wiley & Sons

Page : 242 pages

File Size : 26,12 MB

Release : 2022-01-26

Category : Mathematics

ISBN : 1786306697

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Book Description

This book is entirely devoted to discrete time and provides a detailed introduction to the construction of the rigorous mathematical tools required for the evaluation of options in financial markets. Both theoretical and practical aspects are explored through multiple examples and exercises, for which complete solutions are provided. Particular attention is paid to the Cox, Ross and Rubinstein model in discrete time. The book offers a combination of mathematical teaching and numerous exercises for wide appeal. It is a useful reference for students at the master’s or doctoral level who are specializing in applied mathematics or finance as well as teachers, researchers in the field of economics or actuarial science, or professionals working in the various financial sectors. Martingales and Financial Mathematics in Discrete Time is also for anyone who may be interested in a rigorous and accessible mathematical construction of the tools and concepts used in financial mathematics, or in the application of the martingale theory in finance



Martingale Methods in Financial Modelling

Author : Marek Musiela

Publisher : Springer Science & Business Media

Page : 521 pages

File Size : 50,48 MB

Release : 2013-06-29

Category : Mathematics

ISBN : 3662221322

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Book Description

A comprehensive and self-contained treatment of the theory and practice of option pricing. The role of martingale methods in financial modeling is exposed. The emphasis is on using arbitrage-free models already accepted by the market as well as on building the new ones. Standard calls and puts together with numerous examples of exotic options such as barriers and quantos, for example on stocks, indices, currencies and interest rates are analysed. The importance of choosing a convenient numeraire in price calculations is explained. Mathematical and financial language is used so as to bring mathematicians closer to practical problems of finance and presenting to the industry useful maths tools.



Mathematics of Financial Markets

Author : Robert J Elliott

Publisher : Springer Science & Business Media

Page : 298 pages

File Size : 42,94 MB

Release : 2013-11-11

Category : Mathematics

ISBN : 1475771460

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Book Description

This book explores the mathematics that underpins pricing models for derivative securities such as options, futures and swaps in modern markets. Models built upon the famous Black-Scholes theory require sophisticated mathematical tools drawn from modern stochastic calculus. However, many of the underlying ideas can be explained more simply within a discrete-time framework. This is developed extensively in this substantially revised second edition to motivate the technically more demanding continuous-time theory.



An Introduction to the Mathematics of Financial Derivatives

Author : Salih N. Neftci

Publisher : Academic Press

Page : 550 pages

File Size : 48,54 MB

Release : 2000-05-19

Category : Business & Economics

ISBN : 0125153929

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Book Description

A step-by-step explanation of the mathematical models used to price derivatives. For this second edition, Salih Neftci has expanded one chapter, added six new ones, and inserted chapter-concluding exercises. He does not assume that the reader has a thorough mathematical background. His explanations of financial calculus seek to be simple and perceptive.



Introduction to Stochastic Finance

Author : Jia-An Yan

Publisher : Springer

Page : 406 pages

File Size : 20,5 MB

Release : 2018-10-10

Category : Mathematics

ISBN : 9811316570

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Book Description

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.



Stochastic Calculus and Financial Applications

Author : J. Michael Steele

Publisher : Springer Science & Business Media

Page : 303 pages

File Size : 41,74 MB

Release : 2012-12-06

Category : Mathematics

ISBN : 1468493051

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Book Description

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



Stochastic Financial Models

Author : Douglas Kennedy

Publisher : CRC Press

Page : 264 pages

File Size : 48,63 MB

Release : 2016-04-19

Category : Business & Economics

ISBN : 1439882711

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Book Description

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



Financial Calculus

Author : Martin Baxter

Publisher : Cambridge University Press

Page : 252 pages

File Size : 43,59 MB

Release : 1996-09-19

Category : Business & Economics

ISBN : 9780521552899

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Book Description

A rigorous introduction to the mathematics of pricing, construction and hedging of derivative securities.



PDE and Martingale Methods in Option Pricing

Author : Andrea Pascucci

Publisher : Springer Science & Business Media

Page : 727 pages

File Size : 15,63 MB

Release : 2011-04-15

Category : Mathematics

ISBN : 8847017815

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Book Description

This book offers an introduction to the mathematical, probabilistic and numerical methods used in the modern theory of option pricing. The text is designed for readers with a basic mathematical background. The first part contains a presentation of the arbitrage theory in discrete time. In the second part, the theories of stochastic calculus and parabolic PDEs are developed in detail and the classical arbitrage theory is analyzed in a Markovian setting by means of of PDEs techniques. After the martingale representation theorems and the Girsanov theory have been presented, arbitrage pricing is revisited in the martingale theory optics. General tools from PDE and martingale theories are also used in the analysis of volatility modeling. The book also contains an Introduction to Lévy processes and Malliavin calculus. The last part is devoted to the description of the numerical methods used in option pricing: Monte Carlo, binomial trees, finite differences and Fourier transform.



Financial Statistics and Mathematical Finance

Author : Ansgar Steland

Publisher : John Wiley & Sons

Page : 355 pages

File Size : 23,68 MB

Release : 2012-06-21

Category : Business & Economics

ISBN : 1118316568

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Book Description

Mathematical finance has grown into a huge area of research which requires a lot of care and a large number of sophisticated mathematical tools. Mathematically rigorous and yet accessible to advanced level practitioners and mathematicians alike, it considers various aspects of the application of statistical methods in finance and illustrates some of the many ways that statistical tools are used in financial applications. Financial Statistics and Mathematical Finance: Provides an introduction to the basics of financial statistics and mathematical finance. Explains the use and importance of statistical methods in econometrics and financial engineering. Illustrates the importance of derivatives and calculus to aid understanding in methods and results. Looks at advanced topics such as martingale theory, stochastic processes and stochastic integration. Features examples throughout to illustrate applications in mathematical and statistical finance. Is supported by an accompanying website featuring R code and data sets. Financial Statistics and Mathematical Finance introduces the financial methodology and the relevant mathematical tools in a style that is both mathematically rigorous and yet accessible to advanced level practitioners and mathematicians alike, both graduate students and researchers in statistics, finance, econometrics and business administration will benefit from this book.