We introduce a model of super-exponential financial bubbles with two assets (risky and risk-free), in which fundamentalist and chartist traders co-exist. Fundamentalists form expectations on the return and risk of a risky asset and maximize their constant relative risk aversion expected utility...

By combining (i) the economic theory of rational expectation bubbles, (ii) behavioral finance on imitation and herding of investors and traders and (iii) the mathematical and statistical physics of bifurcations and phase transitions, the log-periodic power law (LPPL) model has been developed as...

We present a new theory of homogeneous volatility (and variance) estimators for arbitrary stochastic processes. The main tool of our theory is the parsimonious encoding of all the information contained in the OHLC prices for a given time interval by the joint distributions of the high-minusopen,...

By combining (i) the economic theory of rational expectation bubbles, (ii) behavioral finance on imitation and herding of investors and traders and (iii) the mathematical and statistical physics of bifurcations and phase transitions, the logperiodic power law (LPPL) model has been developed as a...

We develop the concept of “dragon-kings” corresponding to meaningful outliers, which are found to coexist with power laws in the distributions of event sizes under a broad range of conditions in a large variety of systems. These dragon-kings reveal the existence of mechanisms of...

We present a simple agent-based model to study how the proximate triggering factor of a crash or a rally might relate to its fundamental mechanism, and vice versa. Our agents form opinions and invest, based on three sources of information, (i) public information, i.e. news, (ii) information from...

Episodes of market crashes have fascinated economists for centuries. Although many academics, practitioners and policy makers have studied questions related to collapsing asset price bubbles, there is little consensus yet about their causes and effects. This review and essay evaluates some of...

The heavy-tailed distribution of firm sizes first discovered by Zipf (1949) is one of the best established empirical facts in economics. We show that it has strong implications for asset pricing. Due to the concentration of the market portfolio when the distribution of the capitalization of...