Self-organized “slimming” of power law tails by increasing market returns

We introduce a simple generalization of rational bubble models which removes the fundamental problem discovered by [Lux and Sornette, 1999] that the distribution of returns is a power law with exponent less than 1, in contradiction with empirical data. Our model predicts that, the higher is the market remuneration above the discount rate, the thinner is the tail of price returns but the larger is the volatility. Financial markets seem to have self-organized to balance “small” and extreme risks.