Gaussian Distributions .. the building block of Risk management OR the building block of a financial CRISIS

I came to this topic as someone who understands a bit of statistics and a bit of engineering. The usual way to get Gaussian fluctuations is to add up lots of independent little fluctuations (the central limit theorem). The little ones (the individual traders in a market) have to act independently of each other, or the theorem doesn't follow. Obviously, in real markets, the traders' behavior is influenced by the actions of other traders. In the aggregate system, small fluctuations about the mean will still often be Gaussian, but that doesn't mean the big ones are. It was Mandelbrot that discovered "fat tails", that very extreme price movements are far more likely than the theories predict. His findings were initially rejected, and continued to be resisted even when they were replicated in other markets (and then proved out in the real world: a daily price move like that of the 1987 crash was so extreme as to verge on being statistically impossible). 

As a practical matter, non-Gaussian 1/f noise (as opposed to Gaussian -white noise) has been well known to radio engineers since the 1920s and 1930s.

I was shocked when I read a vice-chairman of the Fed , at the time of the LTCM breakup, saying that information feedback is always a stabilizing factor. Any engineer who has studied control theory knows the opposite is true. The math of control theory was first developed by Maxwell (his equations still haunt me), who studied a lever arm connecting a pressure gauge on a steam boiler back to the feed at the bottom of the coal hopper (for that reason called feedback). If the pivot is too close to the boiler (too much feedback), the boiler goes into uncontrolled oscillations and explodes.

Recently, I read a friend's blog whose batchmate from college had become a quant on Wall Street. He said, ofcourse they know that fluctuations aren't Gaussian, but Gaussian fluctuations are the only ones they could model. They're paid to develop models like everyone else's models, not to develop models that are correct !! Shocking but very true. I believe that his revelation is also pervasive because if anybody models in the fat tails, as against the market, the risk premium would be comparatively high, which means costlier end products and little or no sales.

Sometimes I feel that in the race to become effecient, we manipulate facts in our favour and undermine basic risks...