**Proceedings of Symposia in Applied Mathematics**

Volume: 57;
1999;
167 pp;
Hardcover

MSC: Primary 91;
Secondary 60; 93

Print ISBN: 978-0-8218-0751-4

Product Code: PSAPM/57

List Price: $38.00

Individual Member Price: $30.40

**Electronic ISBN: 978-0-8218-9272-5
Product Code: PSAPM/57.E**

List Price: $38.00

Individual Member Price: $30.40

# Introduction to Mathematical Finance

Share this page *Edited by *
*David C. Heath; Glen Swindle*

The foundation for the subject of mathematical finance was laid nearly 100
years ago by Bachelier in his fundamental work, Théorie de la
spéculation. In this work, he provided the first treatment of Brownian
motion. Since then, the research of Markowitz, and then of Black, Merton,
Scholes, and Samuelson brought remarkable and important strides in the field. A
few years later, Harrison and Kreps demonstrated the fundamental role of
martingales and stochastic analysis in constructing and understanding models
for financial markets. The connection opened the door for a flood of
mathematical developments and growth.

Concurrently with these mathematical advances, markets have grown, and
developments in both academia and industry continue to expand. This lively
activity inspired an AMS Short Course at the Joint Mathematics Meetings in San
Diego (CA).

The present volume includes the written results of that course. Articles are
featured by an impressive list of recognized researchers and
practitioners. Their contributions present deep results, pose challenging
questions, and suggest directions for future research. This collection offers
compelling introductory articles on this new, exciting, and rapidly growing
field.

#### Readership

Graduate students, and applied and research mathematicians interested in mathematical finance; physicists; engineers.

# Table of Contents

## Introduction to Mathematical Finance

- Contents vii8 free
- Preface ix10 free
- Quantitative methods for portfolio management 112 free
- An introduction to option pricing and the mathematical theory of risk 2536
- Non-arbitrage and the fundamental theorem of asset pricing: Summary of main results 4960
- Introduction to models for the evolution of the term structure of interest rates 5970
- Transition densities for interest rate and other nonlinear diffusions 6576
- Transaction costs in portfolio management and derivative pricing 101112
- Index 165176