Systematic and multifactor risk models revisited

Systematic and multifactor risk models are revisited via methods which were already successfully developed in signal processing and in automatic control. The results, which bypass the usual criticisms on those risk modeling, are illustrated by several successful computer experiments.Comment: First Paris Financial Management Conference, Paris : France (2013

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 r\^ole of probability theory

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

Delta hedging, which plays a crucial r\^ole 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.Comment: 18th Mediterranean Conference on Control and Automation, Marrakech : Morocco (2010

Stability margins and model-free control: A first look

We show that the open-loop transfer functions and the stability margins may be defined within the recent model-free control setting. Several convincing computer experiments are presented including one which studies the robustness with respect to delays.Comment: 13th European Control Conference, Strasbourg : France (2014

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.Comment: 1st International Conference on Systems and Computer Science, Villeneuve d'Ascq : France (2012

Towards New Technical Indicators for Trading Systems and Risk Management

We derive two new technical indicators for trading systems and risk management. They stem from trends in time series, the existence of which has been recently mathematically demonstrated by the same authors (A mathematical proof of the existence of trends in financial time series, Proc. Int. Conf. Systems Theory: Modelling, Analysis and Control, Fes, 2009), and from higher order quantities which replace the familiar statistical tools. Recent fast estimation techniques of algebraic flavor are utilized. The first indicator tells us if the future price will be above or below the forecasted trendline. The second one predicts abrupt changes. Several promising numerical experiments are detailed and commented.Quantitative Finance, technical analysis, trading systems, risk management, trends, technical indicators, time series

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

Systematic risk analysis: first steps towards a new definition of beta

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 trends in financial time series, Proc. Int. Conf. Systems Theory: Modelling, Analysis and Control, Fes, 2009, online: http://hal.inria.fr/inria-00352834/en/) leads to convincing computer experiments which are easily implementable.Quantitative finance; risk analysis; beta; alpha; trends; technical analysis; estimation techniques; forecasting; abrupt changes; nonstandard analysis.

On short-term traffic flow forecasting and its reliability

Recent advances in time series, where deterministic and stochastic modelings as well as the storage and analysis of big data are useless, permit a new approach to short-term traffic flow forecasting and to its reliability, i.e., to the traffic volatility. Several convincing computer simulations, which utilize concrete data, are presented and discussed.Comment: 8th IFAC Conference on Manufacturing Modeling, Management & Control (Troyes, France, June 2016

"Intelligent" controllers on cheap and small programmable devices

It is shown that the "intelligent" controllers which are associated to the recently introduced model-free control synthesis may be easily implemented on cheap and small programmable devices. Several successful numerical experiments are presented with a special emphasis on fault tolerant control