Most modern financial markets use a continuous double auction mechanism to store and match orders and facilitate trading. In this paper we develop a microscopic dynamical statistical model for the continuous double auction under the assumption of IID random order flow, and analyse it using...

It is widely believed that fluctuations in transaction volume, as reflected in the number of transactions and to a lesser extent their size, are the main cause of clustered volatility. Under this view bursts of rapid or slow price diffusion reflect bursts of frequent or less frequent trading,...

We study the cause of large fluctuations in prices on the London Stock Exchange. This is done at the microscopic level of individual events, where an event is the placement or cancellation of an order to buy or sell. We show that price fluctuations caused by individual market orders are...

Based on a recent model of shearing granular media we propose a new mechanism for slow dynamics. It consists of two main steps: A global optimization and a restructuring. We present numerical results of the model and its analytical treatment on the hierarchical lattice. A simplified local...

We introduce a simple lattice model for the formation and evolution of shear bands in granular media. We study this model by numerical simulations and find that due to the localization of the shear band and the consequent inhomogeneous aging of the material, the average density shows very...

"Stress tests are the most innovative regulatory tool to prevent and fight financial crises. Their use has fundamentally changed the mathematical modeling of financial systems, financial risk management in the public and private sector, and the policies designed to prevent and mitigate financial...