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Inequality and finance; differences between Bachelier and Mandelbrot


My approach to finance
Benoît Mandelbrot Mathematician
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But let me stop perhaps to motivate my approach to finance, by comparison with other people's approaches and with other people's, how should I say, wishes. The hope of very many people is to predict when the next big change will occur, because they want to take advantage of it by either selling or buying. Now that, I think, is completely outside of the hope of any mathematical scenario. The exact date of these events is not part of something I hope to do. I don't think that anybody has come close in this fashion, and I'm simply not focused on it because I don't think there'll be much hope of it. Many people believe that good science requires complete explanation; that if a phenomenon can't be explained it cannot be tackled unless it's fully explained on the basis of reduction to some fundamental laws. Physics has many examples of reduction. There are some theories like relativity theory and quantum theory, which certainly reduce very complicated phenomena to principles that are declared to be irreducible. Those principles are by no means obvious, by no means overwhelmingly true. But if I assume they are true, everything else follows, and the idea of reductionism is at the centre of science. In economics, however, there are no laws comparable to those of physics. Nothing comes close. Therefore to hope for reduction and to expect reduction to occur is, I think, asking for too much. And there is an attitude which is very widespread, which is that of theoreticians who say, "Well, the Holy Grail, or bust. Either I succeed regarding this idea of explanation of everything on the base of simple principles, or if not, I give up." I think this idea is very bad, very poor, and very unfortunate tactically. We have an enormous quantity of data for finance. In fact, in my work in finance, in technical terms, I can have easily a spread of time scales from one to a thousand or ten thousand or more, which means three or four orders of magnitude. Three or four orders of magnitude is a very substantial scale by the standards of any field. Sometimes I have more than three orders of magnitude. It is not a case in which one has only very narrow scales, very short records or very bad data: for prices now one can have records every minute for many years if one wishes. Therefore data is very abundant. For the purpose of measuring risks inherent in many financial instruments, explanation is probably irrelevant. The main question is to evaluate those risks. In typical cases the Bachelier model would say that the risk of a certain event occurring is 10 to the -3, -4, -5, sometimes -10, which means extraordinarily small. I said a ten sigma change in a Gaussian price with high probability of 10 to the-23, the inverse of Avagadro's number: it would effectively never happen.

Benoît Mandelbrot (1924-2010) discovered his ability to think about mathematics in images while working with the French Resistance during the Second World War, and is famous for his work on fractal geometry - the maths of the shapes found in nature.

Listeners: Daniel Zajdenweber Bernard Sapoval

Daniel Zajdenweber is a Professor at the College of Economics, University of Paris.

Bernard Sapoval is Research Director at C.N.R.S. Since 1983 his work has focused on the physics of fractals and irregular systems and structures and properties in general. The main themes are the fractal structure of diffusion fronts, the concept of percolation in a gradient, random walks in a probability gradient as a method to calculate the threshold of percolation in two dimensions, the concept of intercalation and invasion noise, observed, for example, in the absorbance of a liquid in a porous substance, prediction of the fractal dimension of certain corrosion figures, the possibility of increasing sharpness in fuzzy images by a numerical analysis using the concept of percolation in a gradient, calculation of the way a fractal model will respond to external stimulus and the correspondence between the electrochemical response of an irregular electrode and the absorbance of a membrane of the same geometry.

Duration: 3 minutes, 44 seconds

Date story recorded: May 1998

Date story went live: 29 September 2010