We introduce the concept of “negative bubbles” as the mirror image of standard financial bubbles, in which positive feedback mechanisms may lead to transient accelerating price falls. To model these negative bubbles, we adapt the Johansen-Ledoit-Sornette (JLS) model of rational expectation...

We present an extension of the Johansen-Ledoit-Sornette (JLS) model to include an additional pricing factor called the Zipf factorʺ, which describes the diversification risk of the stock market portfolio. Keeping all the dynamical characteristics of a bubble described in the JLS model, the new...

The Johansen-Ledoit-Sornette (JLS) model of rational expectation bubbles with finite-time singular crash hazard rates has been developed to describe the dynamics of financial bubbles and crashes. It has been applied successfully to a large variety of financial bubbles in many different markets....