We utilize the existence of trends for financial time series (Fliess M., Join C.: A Mathematical Proof of the Existence of Trends in Financial Time Series, http://ssrn.com/abstract=1459662) in order to propose a model-free setting for delta hedging. It avoids most of the shortcomings encountered...

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.,...