Mathematical Finance and Probability

1. Front Matter

   Pages i-ix

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2. Introduction

   • E. Briys, F. De Varenne

   Pages 1-6

3. A Short Primer on Finance

   • H. R. Varian

   Pages 7-39

4. Positive Linear Functionals

   • H. Dybvig, S. A. Ross

   Pages 41-72

5. Finite Probability Spaces

   • M. Kline

   Pages 73-87

6. Random Variables

   • B. A. Russell

   Pages 89-109

7. General One-Period Models

   • J. E. Ingersoll Jr.

   Pages 111-128

8. Information and Randomness

   • A. S. Eddington

   Pages 129-145

9. Independence

   • A. N. Kolmogorov

   Pages 147-160

10. Multi-Period Models:The Main Issues

    • R. C. Merton

    Pages 161-177

11. Conditioning and Martingales

    • J. M. Harrison, S. R. Pliska

    Pages 179-190

12. The Fundamental Theorems of Asset Pricing

    • H. Dybvig, S. A. Ross

    Pages 191-199

13. The Cox—Ross—Rubinstein Model

    • J. C. Cox, S. A. Ross, M. Rubinstein

    Pages 201-219

14. The Central Limit Theorem

    • F. Galton

    Pages 221-246

15. The Black—Scholes Formula

    • J. C. Cox, S. A. Ross, M. Rubinstein

    Pages 247-255

16. Optimal Stopping

    • K. L. Chung

    Pages 257-275

17. American Claims

    • R. Myneni

    Pages 277-295

18. Back Matter

    Pages 297-328

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On what grounds can one reasonably expect that a complex financial contract solving a complex real-world issue does not deserve the same thorough scientific treatment as an aeroplane wing or a micro-proces­ sor? Only ignorance would suggest such an idea. E. Briys and F. De Varenne The objective of this book is to give a self-contained presentation of that part of mathematical finance devoted to the pricing of derivative instruments. During the past two decades the pricing of financial derivatives - or more generally: mathematical finance - has steadily won in importance both within the financial services industry and within the academic world. The complexity of the mathemat­ ics needed to master derivatives techniques naturally resulted in a high demand for quantitatively oriented professionals (mostly mathematicians and physicists) in the banking and insurance world. This in turn triggered a demand for university courses on the relevant topics and at the same time confronted the mathematical community with an interesting field of application for many techniques that had originally been developed for other purposes. Most probably this development was accelerated by an ever more applied orientation of the mathematics curriculum and the fact that finance institutions were often willing to generously support research in this field.

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

 "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 modernprobability 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

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