BUBBLES AND CRASHES IN FINANCE: A PHASE TRANSITION FROM RANDOM TO DETERMINISTIC BEHAVIOUR IN PRICES
BUBBLES AND CRASHES IN FINANCE: A PHASE TRANSITION FROM RANDOM TO DETERMINISTIC BEHAVIOUR IN PRICES

Summary/Abstract: We develop a rational expectations model of financial bubbles and study how the risk-return interplay is incorporated into prices. We retain the interpretation of the leading Johansen-Ledoit-Sornette model: namely, that the price must rise prior to a crash in order to compensate a representative investor for the level of risk. This is accompanied, in our stochastic model, by an illusion of certainty as described by a decreasing volatility function. As the volatility function goes to zero, crashes can be seen to represent a phase transition from stochastic to deterministic behaviour in prices.

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