Benoit Mandelbrot: A personal tribute (2011)
(Published by JP Bouchaud | April 2024)
Benoit has always been one of my super-heroes, along with Pierre-Gilles de Gennes and Phil Anderson, father figures who have guided and enlightened my own scientific trail. I have been intellectually aroused by almost everything Benoit has worked on – starting with Lévy flights and stable laws, which eventually triggered my interest in finance. He attended one of the very first finance talks I gave in 1994, and his support at the time was crucial.
I have been deeply influenced by Benoit’s concept of statistical concentration (I like to call it “condensation”) that pervades, often thanks to him, so many fields, from economics to ecology, from finance to turbulence, from quantum insulators to the physics of glasses. He launched so many balloons behind which I saw myself running: fractional Brownian motions, Zipf plots, multi-fractals (and their application to financial time series), etc.
But what I admire most is his genuine curiosity for empirical data, and the role that data analysis played in his intellectual journey – quite remarkable for a mathematician. He was of course the first one to take seriously the presence of fat tails and long memory in financial data, and he wisely demurred when the Brownian “virus” (as Christian Walter calls it) spread across the financial mathematics community. The technical paraphernalia available to deal with Brownian motion was just too beautiful and too congenial to allow Mandelbrot ruining it all!
It took the 1987 crash to realize that Benoit was maybe not an old curmudgeon and that serious research on fat tails and long memory was indeed badly needed. I have myself repeatedly ranted against the Black-Scholes dogma and the lack of empirically grounded models in finance. I now realize how far ahead Benoit was: a rare harbinger, original and creative, exploring the (fractal) boundaries of knowledge, relentlessly challenging the accepted lore.
His work is the incarnation of Marcel Proust’s sentence:
Les paradoxes d’aujourd’hui sont les préjugés de demain.
Finally, I want to mention another empirical work of Benoit’s that is probably not known in the quantitative finance circles. In 1984, Mandelbrot, Passoja & Paullay published a pioneering experimental paper on the fractal nature of fracture surfaces.
My wife, Bouchaud Elisabeth (now actress and playwright), was an early follower of their work and spent 20 years scrutinizing and deciphering the exquisitely complex statistics of these rough surfaces (see picture below of a synthetic fractal landscape). I tried to help on the modelling side, and we published together “Models of Fractal Cracks” in 1994.
We have been particularly lucky to share this long-lasting passion, on top of all the others. For this and for the rest, I want to thank Benoit for having had such an impact on my life.
#fractals #finance #models #cracks