Solving Stochastic Money-in-the-Utility-Function Models

Abstract

This paper analyzes the necessary and su¢ cient conditions for solving money-inthe-utility-function models when contemporaneous asset returns are uncertain. A unique solution to such models is shown to exist under certain measurability conditions. Stochastic Euler equations, whose existence is normally assumed in these models, are then formally derived. The regularity conditions are weak, and economically innocuous. The results apply to the broad range of discrete-time monetary and …nancial models that are special cases of the model used in this paper. The method is also applicable to other dynamic models that incorporate contemporaneous uncertainty.