A new standpoint on financial time series, without the use of any mathematical model and of probabilistic tools, yields not only a rigorous approach of trends and volatility, but also efficient calculations which were already successfully applied in automatic control and in signal processing. It...

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,...

We suggest a new model-free definition of the beta coefficient, which plays an important rôle in systematic risk management. This setting, which is based on the existence of trends for financial time series via nonstandard analysis (Fliess M., Join C.: A Mathematical Proof of the Existence of...

This work is settling a longstanding quarrel in quantitative finance by proving the existence of trends in financial time series thanks to a theorem due to P. Cartier and Y. Perrin, which is expressed in the language of nonstandard analysis (Integration over finite sets, F. & M. Diener, eds.,...

In this paper, we shed light on the selection of the benefi ciaries from the French competitiveness cluster policy which was launched in 2005 and extended to 2012. We disentangle the selection and self-selection eff ects, as emphasized in the theoretical literature on regional and industrial...