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Introduction to the Mathematics of Finance
 
R. J. Williams University of California, San Diego, La Jolla, CA
Front Cover for Introduction to the Mathematics of Finance
Available Formats:
Hardcover ISBN: 978-0-8218-3903-4
Product Code: GSM/72
List Price: $45.00
MAA Member Price: $40.50
AMS Member Price: $36.00
Softcover ISBN: 978-1-4704-6038-9
Product Code: GSM/72.S
List Price: $45.00
MAA Member Price: $40.50
AMS Member Price: $36.00
Electronic ISBN: 978-1-4704-1805-2
Product Code: GSM/72.E
List Price: $42.00
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AMS Member Price: $33.60
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List Price: $67.50
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Front Cover for Introduction to the Mathematics of Finance
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  • Front Cover for Introduction to the Mathematics of Finance
  • Back Cover for Introduction to the Mathematics of Finance
Introduction to the Mathematics of Finance
R. J. Williams University of California, San Diego, La Jolla, CA
Available Formats:
Hardcover ISBN:  978-0-8218-3903-4
Product Code:  GSM/72
List Price: $45.00
MAA Member Price: $40.50
AMS Member Price: $36.00
Softcover ISBN:  978-1-4704-6038-9
Product Code:  GSM/72.S
List Price: $45.00
MAA Member Price: $40.50
AMS Member Price: $36.00
Electronic ISBN:  978-1-4704-1805-2
Product Code:  GSM/72.E
List Price: $42.00
MAA Member Price: $37.80
AMS Member Price: $33.60
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $67.50
MAA Member Price: $60.75
AMS Member Price: $54.00
List Price: $67.50
MAA Member Price: $60.75
AMS Member Price: $54.00
  • Book Details
     
     
    Graduate Studies in Mathematics
    Volume: 722006; 150 pp
    MSC: Primary 60; 62; 91; Secondary 58;

    The modern subject of mathematical finance has undergone considerable development, both in theory and practice, since the seminal work of Black and Scholes appeared a third of a century ago. This book is intended as an introduction to some elements of the theory that will enable students and researchers to go on to read more advanced texts and research papers.

    The book begins with the development of the basic ideas of hedging and pricing of European and American derivatives in the discrete (i.e., discrete time and discrete state) setting of binomial tree models. Then a general discrete finite market model is introduced, and the fundamental theorems of asset pricing are proved in this setting. Tools from probability such as conditional expectation, filtration, (super)martingale, equivalent martingale measure, and martingale representation are all used first in this simple discrete framework. This provides a bridge to the continuous (time and state) setting, which requires the additional concepts of Brownian motion and stochastic calculus. The simplest model in the continuous setting is the famous Black-Scholes model, for which pricing and hedging of European and American derivatives are developed. The book concludes with a description of the fundamental theorems for a continuous market model that generalizes the simple Black-Scholes model in several directions.

    Readership

    Graduate students interested in financial mathematics.

  • Table of Contents
     
     
    • Chapters
    • Chapter 1. Financial markets and derivatives
    • Chapter 2. Binomial model
    • Chapter 3. Finite market model
    • Chapter 4. Black-Scholes model
    • Chapter 5. Multi-dimensional Black-Scholes model
    • Appendix A. Conditional expectation and $L^p$-spaces
    • Appendix B. Discrete time stochastic processes
    • Appendix C. Continuous time stochastic processes
    • Appendix D. Brownian motion and stochastic integration
  • Reviews
     
     
    • This monograph gives a far-reaching and easily readable advanced introduction to the mathematical modelling of the absence of riskless financial profits, as well as to the connected topic of pricing and risk-protecting-replication/hedging of securities whose value depend on an underlying asset. ...The book's style is pragmatic, precise, concise, with smoothly and fast increasing technical level including the quotation of mathematical subtleties.

      Wolfgang Stummer
    • The text is clearly written and well-arranged and most of the results are proved in detail. Each chapter is completed with exercises, which makes the textbook very comprehensive.

      EMS Newsletter
  • Request Review Copy
  • Get Permissions
Volume: 722006; 150 pp
MSC: Primary 60; 62; 91; Secondary 58;

The modern subject of mathematical finance has undergone considerable development, both in theory and practice, since the seminal work of Black and Scholes appeared a third of a century ago. This book is intended as an introduction to some elements of the theory that will enable students and researchers to go on to read more advanced texts and research papers.

The book begins with the development of the basic ideas of hedging and pricing of European and American derivatives in the discrete (i.e., discrete time and discrete state) setting of binomial tree models. Then a general discrete finite market model is introduced, and the fundamental theorems of asset pricing are proved in this setting. Tools from probability such as conditional expectation, filtration, (super)martingale, equivalent martingale measure, and martingale representation are all used first in this simple discrete framework. This provides a bridge to the continuous (time and state) setting, which requires the additional concepts of Brownian motion and stochastic calculus. The simplest model in the continuous setting is the famous Black-Scholes model, for which pricing and hedging of European and American derivatives are developed. The book concludes with a description of the fundamental theorems for a continuous market model that generalizes the simple Black-Scholes model in several directions.

Readership

Graduate students interested in financial mathematics.

  • Chapters
  • Chapter 1. Financial markets and derivatives
  • Chapter 2. Binomial model
  • Chapter 3. Finite market model
  • Chapter 4. Black-Scholes model
  • Chapter 5. Multi-dimensional Black-Scholes model
  • Appendix A. Conditional expectation and $L^p$-spaces
  • Appendix B. Discrete time stochastic processes
  • Appendix C. Continuous time stochastic processes
  • Appendix D. Brownian motion and stochastic integration
  • This monograph gives a far-reaching and easily readable advanced introduction to the mathematical modelling of the absence of riskless financial profits, as well as to the connected topic of pricing and risk-protecting-replication/hedging of securities whose value depend on an underlying asset. ...The book's style is pragmatic, precise, concise, with smoothly and fast increasing technical level including the quotation of mathematical subtleties.

    Wolfgang Stummer
  • The text is clearly written and well-arranged and most of the results are proved in detail. Each chapter is completed with exercises, which makes the textbook very comprehensive.

    EMS Newsletter
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