arXiv subjects
Publications and source records attributed to Didier Sornette.
We present a theory of option pricing and hedging, designed to address non-perfect arbitrage, market friction and the presence of `fat' tails. An implied volatility `smile' is predicted. We give precise estimates of the residual risk associated with optimal (but imperfect) hedging.
We present a general conceptual framework for self-organized criticality (SOC), based on the recognition that it is nothing but the expression, ''unfolded'' in a suitable parameter space, of an underlying {\em unstable} dynamical critical point. More precisely, SOC is shown to result from the tuning of the {\em order parameter} to a vanishingly small, but {\em positive} value, thus ensuring that the corresponding control parameter lies exactly at its critical value for the underlying transition. This clarifies the role and nature of the {\em very slow driving rate} common to all systems exhibiting SOC. This mechanism is shown to apply to models of sandpiles, earthquakes, depinning, fractal growth and forest-fires, which have been proposed as examples of SOC.