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NEXT STORY

Interaction between work in physics and economics (Part 1)

RELATED STORIES

Boom and bust; October 19th 1987
Benoît Mandelbrot Mathematician
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You speak about market fluctuation, price fluctuation, but don't you think that the booms and the busts, or the big rise or the big slumps of prices are what is very much a characteristic of these fluctuations, which maybe do not appear with the same intensity in other physical phenomena?

Well, that is precisely the direction in which my work took shortly at that time when I was leaving finance for physics. I had discovered the existence of long term dependency in 1/f noises in those physical phenomena, and that was the first example of this phenomenon in physics, which was otherwise ruled by very, very short memory phenomena, and it was immediately clear that I should look for occurrences of this behaviour in prices. That leads to a certain technique called R/S, which I developed, starting with work of Hurst which confirmed very strongly that prices in addition to having long tails had a great deal of long dependency. And then, booms and busts can take two forms: they can either be instant, or take the form of cycles, where there are periods of great activity and periods of low activity. The question was: does my model of price variation - my initial model of '63 - present cycles, and the answer was; it does not. It has long tails but no cycles. Most people were not particularly focused at that time on the long tails, and a very, very fundamental change in public relation to my work, as well a change in my own relation to my work, occurred precisely on October 19th, 1987, when the New York Stock Exchange had this very drastic episode of prices falling down instantly by a very, very large amount. Instantly what used to be viewed as being a rare phenomenon that one could live without considering very much became question that one had to face at one time or another. I remember very well the week after October 19th seeing my director at IBM who was visiting our part of the building, and telling him, "You see, Ralph, now it's happening as I said it would happen some day. I must get back to economics." And he very strongly told me, "Well by all means, you should go back to it." Later on Gomery wrote a foreword to my book on prices and on finance for this purpose. I was very much aware when I left economics and finance in the '60s that what I had done there could not be accepted immediately, that the profession had to grow through understanding the consequences of the Bachelier model. I will come back to that some time later. Ideas that I had been developing there found a very good realisation in physics, not in mainstream physics, not in physics proper, but in peripheral or not so peripheral domains of physical sciences. I mentioned a few previously and in all of them questions of infinite variance or of infinite time dependence were very, very much welcomed in one fashion or another and became extremely important.

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: Bernard Sapoval Daniel Zajdenweber

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.

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

Duration: 3 minutes, 43 seconds

Date story recorded: May 1998

Date story went live: 29 September 2010