Introduction to Mathematical Finance

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 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.