A crisis event is the dramatic and rapid change in a system that occurs as a result of a complex preparatory stage. Dr. Sornette provided many examples of crisis events. A rupture is an irreversible, abrupt crisis event that has threshold characteristics and is commonly the culmination of processes that are correlated over a broad range of scales. An important aspect of crises is that they are characterized by extreme conditions that are usually thought to be anomalies relative to the standard regime. Dr. Sornette proposes that extreme events are a result of the collective action of a variety of phenomena interacting over a broad range of scales.
Several features characterize the complex systems that produce crisis events.
Dr. Sornette finished his lecture with the mathematical analysis of several examples to illustrate the large-scale cooperative behavior of crisis events. The formalism Dr. Sornette uses to price and hedge large claims accounts for the full probability price distributions and makes no assumptions about the symmetry of the positive and negative tails. An optimal portfolio based on Dr. Sornette's technique would minimize the probability of a loss and maximize the probability of a large gain. Dr. Sornette considers the phenomenology of stock market crashes, a coordinated fall in stock prices, to be an example of a crisis event. He attempts to model the stock market using log-periodic corrections to power laws with complex critical exponents.