Diffusion Processes For Asset Prices Under Bounded Rationality

In modern mathematical finance the evolution of several variables such as asset prices, interest rates, latent factors is described, in a continuous time setting, through stochastic differential equations. Nevertheless, in most of the classic literature, these stochastic differential equations are taken as given, and no much attention has paid to infer them from realistic microeconomic models based on agents' behavior. Recently, a growing literature has proposed to model the stock prices evolution assuming agents heterogeneity, and in particular the presence in the market of both rational and non rational agents. For instance, a microeconomic approach is developed to determine the stochastic differential equation for the stock prices as the equilibrium outcome in a market populated by heterogeneous agents. In this paper, we also look for a microeconomic foundation of the evolution of stock prices in an equilibrium perspective with heterogeneous agents. The main feature of our analysis is that we assume that the agents are not fully rational, i.e. they are characterized by bounded rationality. The result is that the diffusion process for the stock price, obtained in the standard weak limit by means of a suitable time rescaling of the discrete modeling equations , turns out to be a mean reverting process, which fluctuates around agent's expectation process.