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 bubbles with a hazard rate describing the collective buying pressure of noise traders …

We propose an extension of the class of rational expectations bubbles (REBs) to the more general rational beliefs … beliefs can thus account for speculative bubbles, without the need for irrational agents or limits to arbitrage. Many of the … shortcomings of REBs that make rational bubbles implausible can be overcome once we relax the ergodicity requirement. In particular …

We introduce a model of super-exponential financial bubbles with two assets (risky and risk-free), in which …

is able to account for the development of endogenous bubbles and crashes. We distinguish three different regimes …’ opinions are idiosyncratic and no bubbles emerge. Around the critical value of the O(n) vector model, cross sectionally … asynchronous bubbles emerge. Above the critical value, small random price fluctuations may be amplified by noise traders herding …

crash (and rally) discrete jump distributions associated with positive (and negative) bubbles. We assume that crashes tend …, which has been previously proposed as a general definition of bubbles. Our bubble model also allows for a sequence of small …