We consider a financial market model with interacting agents and study the long run behaviour of both aggregate behaviour and equilibrium prices. Investors are heterogeneous in their price expectations and they get stochastic signals about the mood of the market described by the empirical...

We consider the stochastic sequence {Yi}t E N defined recursively by the linear relation Yt+l = AtYt + Bt in a random environment. The environment is described by the stochastic process {(At, Bt ) }t E N and is under the simultaneous control of several agents playing a discounted stochastic...

We consider the stochastic sequence {Yi}t E N defined recursively by the linear relation Yt+l = AtYt + Bt in a random environment. The environment is described by the stochastic process {(At, Bt ) }t E N and is under the simultaneous control of several agents playing a discounted stochastic...

A two-dimensional class of mean-field models that may serve as a minimal model to study the properties of long-range systems in two space dimensions is considered. The statistical equilibrium mechanics is derived in the microcanonical ensemble using Monte Carlo simulations for different...

We calculate the thermodynamic entropy of the mean-field φ4 spin model in the microcanonical ensemble as a function of the energy and magnetization of the model. The entropy and its derivatives are obtained from the theory of large deviations, as well as from Rugh's microcanonical formalism,...

We study the mean-field φ4 model in an external magnetic field in the microcanonical ensemble using two different methods. The first one is based on Rugh's microcanonical formalism and leads to express macroscopic observables, such as temperature, specific heat, magnetization and...

Buckdahn et al. (2009b) introduced a mean-field stochastic differential equation to study the backward stochastic differential equation. The objective of the present paper is to deepen the investigation of such mean-field stochastic differential equations by studying them in a Brownian motion...