A dynamic stochastic model of asset pricing with heterogeneous beliefs

<span style="font-size: 9.5pt"><span style="font-size: 9.5pt">This paper presents a new stochastic model of asset pricing, based on agents with heterogeneous beliefs. Forecasting rules of all agents are characterized by a stochastic term that</span><span style="font-size: 9.5pt">works as an agent-based time dependent weight of the conditional expectation of the fundamental. Since we consider the presence of an imitative behavior between agents, these</span><span style="font-size: 9.5pt">weights depend stochastically on the type-distribution of agents. The resulting dynamical</span><span style="font-size: 9.5pt">system is firstly analyzed in a deterministic framework. Starting from the results obtained</span><span style="font-size: 9.5pt">in the deterministic case, the model is lastly explored by reintroducing randomness. The</span><span style="font-size: 9.5pt">deterministic study aims at providing the existence of a region in the parameters plane</span><span style="font-size: 9.5pt">where the unique possible dynamics is the convergence to a steady state, while complexity</span><span style="font-size: 9.5pt">is exhibited outside such region. This region is also analyzed by reintroducing stochasticity and we provide an explicit formula for its probability measure. Our findings are in</span><span style="font-size: 9.5pt">agreement with the economic meaning of the parameters. Finally, we propose a bayesian</span><span style="font-size: 9.5pt">analysis, in order to explore the distribution of the adjustment term of the proportion of</span><div><span style="font-size: 9.5pt; line-height: 115%">agents.</span></span>