Abstract:
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. Given 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
ditTerent predictors under an AR(l) dividend process.
