Is a probabilistic modeling really useful in financial engineering?

A-t-on vraiment besoin d'un modèle probabiliste en ingénierie financière ?

Michel Fliess (1) , Cédric Join (2, 3) , Frédéric Hatt (4)

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
4 Lucid Capital Management

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 is based on a theorem due to P. Cartier and Y. Perrin, which was published in 1995. The above results are employed for sketching a dynamical portfolio and strategy management, without any global optimization technique. Numerous computer simulations are presented.

Mots clés: Quantitative finance; dynamic portfolio management; strategy; time series; trends; volatility; Kalman filters; noise removal; numerical differentiation; nonstandard analysis

Domaines: Finance quantitative [q-fin.CP]; Gestion de portefeuilles [q-fin.PM]; Ingénierie, finance et science [cs.CE]; Automatique; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]; Logique [math.LO]; Statistiques [math.ST]; Théorie [stat.TH]; Méthodologie [stat.ME]

Michel Fliess, Cédric Join, Frédéric Hatt. A-t-on vraiment besoin d'un modèle probabiliste en ingénierie financière ?. Conférence Méditerranéenne sur l'Ingénierie Sûre des Systèmes Complexes, MISC 2011, May 2011, Agadir, Maroc. ⟨hal-00585152v1⟩