Tag Archive: benoit

Mandelbrot on Markets

In my last post on Benoit Mandelbrot’s final TED talk, I mentioned that he had begun his career in finance. The article ‘Economist’ Obituary Recalls Mandelbrot’s Scrutiny of Financial Markets goes into more detail about this. The article discusses the obituary written in the Economist for Mandelbrot (he died on October 14, 2010).

Benoit Mandelbrot believed that fractals could be used to model financial markets. The Gaussian (normal) distribution had been being used to model financial markets, and if Mandelbrot was correct, the Gaussian distribution would not be an effective means of modeling. While it has not been proven that fractals can be used to model financial markets, it is now widely accepted that such markets are not Gaussian.

In his final TED talk, Benoit Mandelbrot spoke about roughness and fractals. The talk was appropriately titled Benoit Mandelbrot: Fractals and the Art of Roughness. In his talk, Mandelbrot explains how everything in nature is inherently rough (this is exemplified with close up images of things such as cauliflower). By looking at the distances between elements on an object or image, a roughness number can be given which can then be used to generate artificial landscapes and other images. This ability is being used in film making.

More generally, studying roughness allows patterns to be recognized in nature. These patterns can then be applied to studying other things in nature. For instance, fractals helped reconstruct the lung in a way that taught surgeons more about it. This in turn advanced their abilities in treating lung related diseases. Mandelbrot described it as, “A geometry of things which have no geometry.”

Interestingly, Mandelbrot actually began his career in financial mathematics. With the way the economy is today, I guess the stock market is a good place to start a career based on roughness.