25th Ostrom Lecture: Money, Markets and Mathematical Models
7:30 p.m. CUE 203
Robert J. Elliott
The introduction will describe some of the history of financial modeling. Brownian motion is a fundamental stochastic process with applications in many fields, in addition to its central role in mathematical finance. Some related antipodean encounters will be described and the development of Brownian motion as a mathematical construction outlined. The year 2000 was the centenary of Bachelier's thesis in which he attempted to model the behaviour of prices on the Paris Bourse. His work anticipated results of Einstein on diffusion, introducing the heat equation and the process now called Brownian motion. Later work of Paul Samuelson will be mentioned leading to an outline of the Black-Scholes formula for pricing options. Empirically it has been observed that some price processes exhibit long term dependence. Fractional Brownian Motion, a modification of standard Brownian motion, is a process which possesses long term dependence. As an introduction to our second talk fractional Brownian Motion will be described and a modified Black-Scholes formula given.