  The Cartier-Perrin theorem, which was published in 1995 and is expressed in
the language of nonstandard analysis, permits, for the first time perhaps, a
clear-cut mathematical definition of the volatility of a financial asset. It
yields as a byproduct a new understanding of the means of returns, of the beta
coefficient, and of the Sharpe and Treynor ratios. New estimation techniques
from automatic control and signal processing, which were already successfully
applied in quantitative finance, lead to several computer experiments with some
quite convincing forecasts.
