Mathematics of Finance

Abstract

Introduction. The recent Nobel prizes in economics awarded to financial economists confirmed the transition that finance has undergone in the past thirty years, moving from being what one wag called a taxonomy of anecdotes to being one of the more tangential and "softer" areas of economics to occupy center stage. Finance has come of age as a science in large part through the application of the work of Wiener and the other pioneers of the theory of stochastic processes. Diffusion processes have become part of the vocabulary of modern finance. Accompanying this intellectual transformation has been a rare for the social sciences embracing of the practical significance—the engineering side—of finance. A recent article in Scientific American takes note of the hundreds of mathematicians and physicists who have moved to Wall Street, where they make use of quite advanced techniques in applied mathematics that lie at the heart of what has become a $50 trillion industry. If one were to look for the new applications of mathematics one would be hard pressed to find an area where the impact has been more certain or more significant. What I would like to do in this short paper is to give the reader a sense of what this is all about. What is happening on Wall Street and what are these mathematicians and physicists doing? What are the major research paradigms and what comes next?