Mean variance preferences expectations formation and the dynamics of random asset prices

This paper analyzes the dynamics of an explicit random process of prices and price expectations of finitely many assets in an economy with overlapping generations of heterogeneous consumers. They maximize expected utility with respect to subjective transition probabilities defined by Markov kernels which describe the forecasting behavior of agents. Give such forecasting rules (predictors) and an exogenous process of dividends, the evolution of equilibrium asset prices and expectations is described by a random dynamical system in the sense of Arnold (1998). The paper investigates the long-run behavior (stationary solutions) by proving the existence and stability of random fixed points for mean-variance preferences under various predictors, including unbiased predictions, and adaptive, as well as OLS forecasting. An explicit characterization of rational expectations solutions is given, providing a full dynamic characterization of asset price processes for the classical CAPM in the case of stationary OLG economies. Numerical simulations are used to compare the performance of the different predictors under an AR(1) dividend process.