Applied to finance, this type of model, called a logistic model, very obviously has many limitations. It does not take into account all the factors which govern the reality of the evolution of an economic magnitude, whether it is a market index or the establishment of the price of a product. It does however allow a certain regularity to become apparent within the magnitudes studied, and to predict that certain results will occur. But the model does not show when they will take place. ‘Certain colleagues have all the same succeeded in predicting a stock market crash. But then again, there have been so many crashes,’ cautions the mathematician. ‘How do we know that it wasn’t purely a matter of luck? In any case today we have put that to one side. We have done the rounds with it, mathematically speaking. From a general point of view, economic and human phenomena are so complex that I don’t know if we will one day really be able to model them reliably. Nevertheless, from a philosophical perspective, it was valuable to show that it was possible to model, to bring to the forefront certain regularities which seemed a priori completely random, that we could consider integrating the notion of chaos into a purely determinist mathematical model, and to do so in integrating and varying an extra parameter. It is for that reason that we wrote the article ‘Chaos Models in Economics’.’

Full steam ahead towards statistics

If it seems difficult to reliably model economic phenomena subject to numerous unpredictable factors, such as human actions (speculation, fears in times of crisis, demographic changes, political influences, etc.) or natural disasters (which can have a brutal influence on exchange rates or raw materials, for example), numerous mathematicians are still working to approach reality ever closer, but are leaving behind determinist models and more and more taking the direction of statistical or probability models, which take more into account notions of chaos and randomness. In this area, even today and after forty years of existence the Black and Scholes model seems to be the authority. It is used in all the financial markets. This model enables a modelling of stock exchanges according to several conditions and parameters, determining the theoretical value of an option whilst taking into account that this value at time t is the product of a purely stochastic process.

Models and future perspectives for mathematicians

In times of crisis even the boldest are twice as prudent. And the shrewd advice of seasoned mathematicians can prove useful. If there is indeed one point which can be predicted without a model, it is that mathematicians can more and more picture prolific careers outside of teaching. The models applied to the economy are not always reliable, but they allow shadowy areas to be looked into with some seriousness and allow them to be seen more clearly. Insurance companies which work in actuarial research groups, the banks and the financial markets are making greater and greater use of the expertise of mathematicians. More generally the discipline can open outwards to a variety of areas, such as sport, music, agronomy, etc. sparking great interest and revealing to students who have little interest in mathematics vocations which have been well hidden up until now. Jacques Blair has understood this, and is today devoting his time at the end of his career to didactics and rendering his passion accessible to a wider public, notably in working with the French periodical, Tangente.