The fluctuation of stock prices is modelled as a sequence of temporary equilibria on a financial market with different types of agents. We summarize joint work with M. Schweizer on the class of Ornstein-Uhlenbeck processes in a random environment which appears in the diffusion limit. Moreover,...

This paper addresses the statistical properties of time series driven by rational bubbles a la Blanchard and Watson (1982). Using insights on the behavior of multiplicative stochastic processes, we demonstrate that the tails of the unconditional distribution emerging from such bubble processes...

Multi-fractal processes have been proposed as a new formalism for modeling the time series of returns in finance. The major attraction of these processes is their capability of generating various degrees of long-memory in different powers of returns - a feature that has been found to...

Multi-fractal processes have been proposed as a new formalism for modeling the time series of returns in finance. The major attraction of these processes is their capability of generating various degrees of long-memory in different powers of returns - a feature that has been found to...

This note reconsiders divergent results on the extremal behaviour of German stock returns that have been published recently. In particular, recent investigations of this issue have arrived at different conclusions regarding the finiteness of the second moment of the return distributions. Here we...

We present a stochastic simulation model of a prototype financial market. Our market is populated by both noise traders and fundamentalist speculators. The dynamics covers switches in the prevailing mood among noise traders (optimistic or pessimistic) as well as switches of agents between the...