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Michel Fliess

Publications and source records attributed to Michel Fliess.

At least 73 records · Page 4Linked to original sources
arXiv2012

Freeway ramp metering control made easy and efficient

"Model-free" control and the related "intelligent" proportional-integral (PI) controllers are successfully applied to freeway ramp metering control. Implementing moreover the corresponding control strategy is straightforward. Numerical simulations on the other hand need the identification of quite complex quantities like the free flow spêed and the critical density. This is achieved thanks to new estimation techniques where the differentiation of noisy signals plays a key rôle. Several excellent computer simulations are provided and analyzed.

math.OC↗
arXiv2012

Preliminary remarks on option pricing and dynamic hedging

An elementary arbitrage principle and the existence of trends in financial time series, which is based on a theorem published in 1995 by P. Cartier and Y. Perrin, lead to a new understanding of option pricing and dynamic hedging. Intricate problems related to violent behaviors of the underlying, like the existence of jumps, become then quite straightforward by incorporating them into the trends. Several convincing computer experiments are reported.

q-fin.PR↗
arXiv2011

Is a probabilistic modeling really useful in financial engineering? - A-t-on vraiment besoin d'un modèle probabiliste en ingénierie financière ?

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.

q-fin.CP↗
arXiv2011

Nothing is as Practical as a Good Theory: Model-Free Control Rien de plus utile qu'une bonne théorie: la commande sans modèle

The experience gained with numerous successful applications permits to revisit some points of model-free control. The numerical differentiation of noisy signals may be replaced by a real time parameter identification which is much simpler. The strange ubiquity of classic PIDs is explained as well as the almost universal utilization of ultra-local models of order 1. We show that even with a partially known model the utilization of an intelligent PI controller remains profitable. Two examples, an inverted pendulum and a heat exchanger, seem to confirm the superiority of model-free control with respect to sliding modes control and techniques stemming from infinite-dimensional systems, such as delays or partial differential equations. Our paper is illustrated by several computer simulations.

math.OC↗
arXiv2011

Volatility made observable at last

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.

q-fin.CP↗
arXiv2010

A mathematical explanation via "intelligent" PID controllers of the strange ubiquity of PIDs

The ubiquity of PID controllers in the industry has remained mysterious until now. We provide here a mathematical explanation of this strange phenomenon by comparing their sampling with the the one of "intelligent" PID controllers, which were recently introduced. Some computer simulations nevertheless confirm the superiority of the new intelligent feedback design.

math.OC↗
arXiv2010

Delta Hedging in Financial Engineering: Towards a Model-Free Approach

Delta hedging, which plays a crucial rôle in modern financial engineering, is a tracking control design for a "risk-free" management. We utilize the existence of trends in financial time series (Fliess M., Join C.: A mathematical proof of the existence of trends in financial time series, Proc. Int. Conf. Systems Theory: Modelling, Analysis and Control, Fes, 2009. Online: http://hal.inria.fr/inria-00352834/en/) in order to propose a model-free setting for delta hedging. It avoids most of the shortcomings encountered with the now classic Black-Scholes-Merton framework. Several convincing computer simulations are presented. Some of them are dealing with abrupt changes, i.e., jumps.

q-fin.PR↗
arXiv2009

Algebraic Change-Point Detection

Elementary techniques from operational calculus, differential algebra, and noncommutative algebra lead to a new approach for change-point detection, which is an important field of investigation in various areas of applied sciences and engineering. Several successful numerical experiments are presented.

math.NA↗
arXiv2009

Model-free control and intelligent PID controllers: towards a possible trivialization of nonlinear control?

We are introducing a model-free control and a control with a restricted model for finite-dimensional complex systems. This control design may be viewed as a contribution to "intelligent" PID controllers, the tuning of which becomes quite straightforward, even with highly nonlinear and/or time-varying systems. Our main tool is a newly developed numerical differentiation. Differential algebra provides the theoretical framework. Our approach is validated by several numerical experiments.

math.OC↗
arXiv2009

A mathematical proof of the existence of trends in financial time series

We are 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): Nonstandard Analysis in Practice, Springer, 1995, pp. 195--204). Those trends, which might coexist with some altered random walk paradigm and efficient market hypothesis, seem nevertheless difficult to reconcile with the celebrated Black-Scholes model. They are estimated via recent techniques stemming from control and signal theory. Several quite convincing computer simulations on the forecast of various financial quantities are depicted. We conclude by discussing the rôle of probability theory.

q-fin.ST↗
arXiv2008

Time Series Technical Analysis via New Fast Estimation Methods: A Preliminary Study in Mathematical Finance

New fast estimation methods stemming from control theory lead to a fresh look at time series, which bears some resemblance to "technical analysis". The results are applied to a typical object of financial engineering, namely the forecast of foreign exchange rates, via a "model-free" setting, i.e., via repeated identifications of low order linear difference equations on sliding short time windows. Several convincing computer simulations, including the prediction of the position and of the volatility with respect to the forecasted trendline, are provided. $\mathcal{Z}$-transform and differential algebra are the main mathematical tools.

stat.AP↗
arXiv2007

Vers une commande multivariable sans modèle

A control strategy without any precise mathematical model is derived for linear or nonlinear systems which are assumed to be finite-dimensional. Two convincing numerical simulations are provided.

math.OC↗
arXiv2007

Critique du rapport signal à bruit en théorie de l'information -- A critical appraisal of the signal to noise ratio in information theory

The signal to noise ratio, which plays such an important role in information theory, is shown to become pointless in digital communications where - symbols are modulating carriers, which are solutions of linear differential equations with polynomial coefficients, - demodulations is achieved thanks to new algebraic estimation techniques. Operational calculus, differential algebra and nonstandard analysis are the main mathematical tools.

cs.IT↗
arXiv2007

Non-linear estimation is easy

Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic definitions and properties are presented within the framework of differential algebra, which permits to handle system variables and their derivatives of any order. Several academic examples and their computer simulations, with on-line estimations, are illustrating our viewpoint.

cs.CE↗
arXiv2007

Probabilités et fluctuations quantiques (Probabilities and quantum fluctuations)

This note is sketching a simple and natural mathematical construction for explaining the probabilistic nature of quantum mechanics. It employs nonstandard analysis and is based on Feynman's interpretation of the Heisenberg uncertainty principle, i.e., of the quantum fluctuations, which was brought to the forefront in some fractal approaches. It results, as in Nelson's stochastic mechanics, in stochastic differential equations which are deduced from infinitesimal random walks. An extended english abstract gives most of the details.

quant-ph↗
arXiv2006

Approche intrinsèque des fluctuations quantiques en mécanique stochastique (An intrinsic approach of the quantum fluctuations in stochastic mechanics)

This note is answering an old questioning about the Fényes-Nelson stochastic mechanics. The Brownian nature of the quantum fluctuations, which are associated to this mechanics, is deduced from Feynman's interpretation of the Heisenberg uncertainty principle via infinitesimal random walks stemming from nonstandard analysis. It is therefore no more necessary to combine those fluctuations with a background field, which has never been well understood. Most of the technical details are contained in an extended english abstract.

quant-ph↗