Schachermayer: The role of Mathematics in Financial Markets

The Nobel Prize in Economics 1997 has been awarded to R. Merton (Harvard) and M. Scholes (Stanford) for their work on Mathematical Finance, thus recognizing the strong impact of stochastic analysis in today's financial markets. The development was initiated in 1973 with the publication of the celebrated "Black-Scholes Option Pricing Formula" which started a fruitful interaction between the theory of stochastic processes and applications in financial markets. It is worth noting that this interchange of ideas has worked in both directions: on the one hand side the financial industry uses more and more sophisticated mathematical tools, on the other hand the concrete problems arising in finance pose challenging mathematical questions which, e.g., led to the recent renaissance of the "théorie générale des processus stochastiques" as developed in the sixties and seventies.

We shall give an overview of the aspects of stochastic analysis used in Mathematical Finance, starting from L. Bachelier's thesis "Théorie de la spéculation" in 1900, who was the first to define Brownian motion and whose aim was precisely to give an option pricing formula. We shall focus on basic ideas rather than on technicalities and we shall point out the mutual relationship between Mathematical Finance and the more classical field of Actuarial Mathematics.

ICM'98 homepage

Please send suggestions and corrections to: pahlig@zib.de
Last modified: August 26, 1998