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Wednesday, April 11, 2012

Fractals and Finance

Wonderful piece on the application of Mandelbrotian fractals (and Levy distributions) to finance:

http://triplehelixblog.com/2012/04/fractal-finance-a-rogue-mathematician%E2%80%99s-search-for-answers/

an excerpt:
"It was the winter of 1961. When he made this discovery, Mandelbrot was at IBM, studying income distribution patterns between the rich and poor. The Harvard economics department invited him to speak about his work. He walked into the office of his host that day to a surprise. On the chalk-board was a figure with a convex shape that opened to the right. He immediately turned to Professor Hendrik Houthhakker and asked why his diagram was already drawn. Houthhakker was perplexed: ‘These are graphs of cotton prices.’
"The puzzling similarity in pattern between income distribution and cotton prices got Mandelbrot thinking. Was it pure coincidence that the two were spitting images of one another, or was there a deeper truth in the strange connection between the two pictures? And so it was that Mandelbrot was propelled into investigating the mysteries of finance."
and it concludes this way:
"These models, Mandelbrot’s body of work suggests, have caused us to misperceive risk in a dangerous way. His work is a potential explanation to unusual market volatility: it suggests that our notions of ‘usual’ might be incorrect. There are academics who have taken up the baton from Mandelbrot, who died last October. These scholars work to build fractal descriptions of markets, models that take into account the Levy distribution. It remains to be seen how long it will take Wall Street to begin using these Levy-based models."

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