Ergodic Markov equilibrium with incomplete markets and short sales

Abstract

This paper studies recursive exchange economies with short sales. Agents maximize discounted expected utility. The asset structure is general and includes real securities, infinite-lived stocks, options, and other derivatives. The main result shows the existence of a competitive equilibrium process that is stationary and has an invariant ergodic measure. Ergodicity is required in finance for time series analysis of structural asset pricing models. This equilibrium property is difficult to obtain when heterogeneous agents can accumulate debt over time. Bounded marginal utility is shown to be a key condition for ergodicity in this setting.