The scientific study of complex systems has transformed a wide range of disciplines in recent years, enabling researchers in both the natural and social sciences to model and predict phenomena as diverse as earthquakes, global warming, demographic patterns, financial crises, and the failure of...

We introduce a simple generalization of rational bubble models which removes the fundamental problem discovered by Lux and Sornette (J. Money, Credit and Banking, preprint at http://xxx.lanl.gov/abs/cond-mat/9910141) that the distribution of returns is a power law with exponent <1, in contradiction with empirical data. The idea is that the price fluctuations associated with bubbles must on average grow with the mean market return r. When r is larger than the discount rate rδ, the distribution of returns of the observable price, sum of the bubble component and of the fundamental price, exhibits an intermediate tail with an exponent which can be larger than 1. This regime r>rδ corresponds...</1,>

We present a self-consistent model for explosive financial bubbles, which combines a mean-reverting volatility process and a stochastic conditional return which reflects nonlinear positive feedbacks and continuous updates of the investors' beliefs and sentiments. The conditional expected returns...

We present a novel methodology to determine the fundamental value of firms in the social-networking sector, motivated by recent realized IPOs and by reports that suggest sky-high valuations of firms such as Facebook, Groupon, LinkedIn Corp., Pandora Media Inc, Twitter, Zynga. Our valuation of...

We present strong evidence that financial bubbles can be identified ex-ante and that a sharp price increase, when suitably qualified by a bubble indicator called LPPLS confidence, does on average predict unusually low returns going forward. For this, we use a methodology called log-periodic...