His father made his living trading clothing; his mother was a dental surgeon. During his first two school years, he was tutored privately by an uncle who despised rote learning: "Most of my time was spent playing chess, reading maps and learning how to open my eyes to everything around me. The family emigrated from Poland to France in , when he was This happened to a close friend from Paris, Zina Morhange, a physician in a nearby county seat.
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Alejandro Nadal Lightning in the sky does not follow a straight line. Neither the straight lines, nor the smooth curves of that geometry exist in nature. But after the wonderful work of Benoit Mandelbrot it is now possible to get closer to a theory of the manifold wrinkles and rough surfaces that are the stuff of our universe. And our economies. Ten days ago this great mathematician, the creator of fractal geometry and other wonders closely related to chaos theory, passed away.
The word fractal , coined by Mandelbrot, denotes a logical semi-geometric figure that can be divided as many times as desired and every time you zoom in on these smaller fractions you end up looking at a replica of the original figure. The best example of this is the famous Koch snowflake , in which the wrinkles are intimately related to patterns of affinity between the parts and the whole. Another example is the cauliflower: no matter how many times one breaks it up, when the pieces are magnified, the same ruggedness and wrinkles of the whole reappear.
The property of self-similarity emerges even in the tiniest crumbles. In Mandelbrot analyzed the variations of cotton prices on a time series starting in There were two important findings. Instead, the data showed a great frequency of extreme variations. Surprisingly, these patterns of self-similarity were present during the entire period , a violent epoch that had seen a Great Depression and two world wars.
Mandelbrot used his fractal theory to explain the presence of extreme events in Wall Street. The basic idea that relates fractals to financial markets is that the probability of experiencing extreme fluctuations like the ones triggered by herd behavior is greater than what conventional wisdom wants us to believe. This of course delivers a more accurate vision of risk in the world of finance. The central objective in financial markets is to maximize income for a given level of risk.
Standard models for this are based on the premise that the probability of extreme variations of asset prices is very low. These models rely on the assumption that asset price fluctuations are the result of a well-behaved random or stochastic process.
This is why mainstream models such as the infamous Black-Scholes model use normal probabilistic distributions to describe price movements. For all practical purposes, extreme variations can be ignored. Mandelbrot thought this was an awful way to look at financial markets.
For him, the distribution of price movements is not normal and has the property of kurtosis , where fat tails abound. This is a more faithful representation of financial markets: the movements of the Dow index for the past hundred years reveals a troubling frequency of violent movements. Still, conventional models rule out these extreme variations and consider they can only happen every 10, years!
Today, three years after the global crisis erupted, reforms for the financial system are clearly insufficient whether in the guise of the Volcker rule or the Dodd-Frank act.
Mandelbrot confirmed what we know about the instability of markets, especially financial markets. Mandelbrot was not an economist. Perhaps this explains why he tried to study how markets really work. This is better than the flawed year-old research program of an economic theory obsessed with the aim of proving fruitlessly that markets are efficient.
The beauty of fractal geometry knows no boundaries.
His father made his living trading clothing; his mother was a dental surgeon. During his first two school years, he was tutored privately by an uncle who despised rote learning: "Most of my time was spent playing chess, reading maps and learning how to open my eyes to everything around me. The family emigrated from Poland to France in , when he was This happened to a close friend from Paris, Zina Morhange, a physician in a nearby county seat. Simply to eliminate the competition, another physician denounced her
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