The foundation for the subject of mathematical finance was laid nearly 100 years ago by Bachelier in his fundamental work, ""Theorie de la speculation"". 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.
Quantitative methods for portfolio management by S. E. Shreve An introduction to option pricing and the mathematical theory of risk by M. Avellaneda Non-arbitrage and the fundamental theorem of asset pricing: Summary of main results by F. Delbaen and W. Schachermayer Introduction to models for the evolution of the term structure of interest rates by D. Heath Transition densities for interest rate and other nonlinear diffusions by Y. Ait-Sahalia Transaction costs in portfolio management and derivative pricing by T. Zariphopoulou Index.