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1 LIX - Laboratoire d-informatique de l-École polytechnique Palaiseau 2 CRAN - Centre de Recherche en Automatique de Nancy 3 ALIEN - Algebra for Digital Identification and Estimation Inria Lille - Nord Europe, Inria Saclay - Ile de France, Ecole Centrale de Lille, Polytechnique - X, CNRS - Centre National de la Recherche Scientifique : UMR8146 4 Lucid Capital Management

Abstract : 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.

Keywords : Time series quantitative finance trends returns volatility beta coefficient Sharpe ratio Treynor ratio forecasts estimation techniques numerical differentiation nonstandard analysis

Author: Michel Fliess - Cédric Join - Frédéric Hatt -

Source: https://hal.archives-ouvertes.fr/


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