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© 2003

Mathematical Finance and Probability

A Discrete Introduction

Textbook

Table of contents

  1. Front Matter
    Pages i-ix
  2. E. Briys, F. De Varenne
    Pages 1-6
  3. H. R. Varian
    Pages 7-39
  4. H. Dybvig, S. A. Ross
    Pages 41-72
  5. M. Kline
    Pages 73-87
  6. B. A. Russell
    Pages 89-109
  7. J. E. Ingersoll Jr.
    Pages 111-128
  8. A. S. Eddington
    Pages 129-145
  9. A. N. Kolmogorov
    Pages 147-160
  10. R. C. Merton
    Pages 161-177
  11. J. M. Harrison, S. R. Pliska
    Pages 179-190
  12. H. Dybvig, S. A. Ross
    Pages 191-199
  13. J. C. Cox, S. A. Ross, M. Rubinstein
    Pages 201-219
  14. F. Galton
    Pages 221-246
  15. J. C. Cox, S. A. Ross, M. Rubinstein
    Pages 247-255
  16. K. L. Chung
    Pages 257-275
  17. R. Myneni
    Pages 277-295
  18. Back Matter
    Pages 297-328

About this book

Introduction

The objective of this book is to give a self-contained presentation to the theory underlying the valuation of derivative financial instruments, which

is becoming a standard part of the toolbox of professionals in the financial industry. Although a complete derivation of the Black-Scholes

option pricing formula is given, the focus is on finite-time models. Not going for the greatest possible level of generality is greatly rewarded by

a greater insight into the underlying economic ideas, putting the reader in an excellent position to proceed to the more general continuous-time

theory.

The material will be accessible to students and practitioners having a working knowledge of linear algebra and calculus. All additional material

is developed from the very beginning as needed. In particular, the book also offers an introduction to modern probability theory, albeit mostly

within the context of finite sample spaces.

The style of presentation will appeal to financial economics students seeking an elementary but rigorous introduction to the subject; mathematics

and physics students looking for an opportunity to become acquainted with this modern applied topic; and mathematicians, physicists or quantitatively inclined economists working in the financial industry.

Keywords

Asset Pricing Excel Markov Chain Markov Chains Measure Options Portfolio Probability space Probability theory Random variable Stochastic Processes linear algebra

Authors and affiliations

  1. 1.Swiss ReZürichSwitzerland
  2. 2.UBS AGZürichSwitzerland

Bibliographic information

Reviews

 "This is probably the best written book on discrete-time models of mathematical finance. It is self consistent, all notions used in it are carefully defined. That is a mathematical book - by mathematicians and for mathematicians, which also means that its practical applications are restricted. The bibliography is complete. I strongly recommend that title as an introduction to mathematical finance."

— Darius Gatarek (Control and Cybernetics)

 

"The style of presentation will appeal to anyone who is seeking an elementary but rigorous introduction to the pricing of derivative securities. The book is written carefully and is very readable."

—Mathematical Reviews

 

"The book offers a self-contained elementary but rigorous and very clear introduction to the pricing of derivative instruments in discrete time. . . . For the interested reader who has not been exposed to modern probability theory before, the book provides an excellent starting point for studying the theory of derivative pricing. In particular, for a rigorous course on derivative pricing in an economics department or at a business school this introduction seems to be well-suited."

—Zentralblatt Math

 

"The book presents the part of mathematical finance devoted to the pricing of derivative instruments; its basic theme is the study of prices in securities markets in an uncertain environment. . . As the objective of the book is to provide a sound understanding of important issues of modern approaches to mathematical finance, several mathematical models are developed and examined in detail.  The focus is on finite-time models and the highest level of generality is frequently sacrificed for the sake of a greater insight into the underlying economic ideas.  Even when the problems are approached from the mathematical point of view and almost all results are strictly proved, the financial interpretation is always stressed. . . The style of presentation is aimed at students of financial economics, mathematics and physics and at mathematicians, physicists and economists working in financial industry."

—APPLICATIONS OF MATHEMATICS