Existence of Optimal Savings Policies with Imperfect Information and Non-Convexities

Abstract

This paper studies the existence of optimal savings paths in models with imperfect information. The returns on savings or on investment are uncertain and the models may have infinite horizom. The results yield existence when both utilities and the distributions of the random rate of return may vary through time, The cases studied here also include nontrivial non-convexities on both the utility fonctions (which are not necessarily bounded) and the feasible sets of consumption paths which may appear because of incomplete information, externalities or increasing returns. Existence is also established when there is learning about the value that determines the distribution of returns, updated according to previous realizations. The techniques use non-linear functional analysis. The results are obtained by proving compactness continuity theorems of certain non-Iinear operators on Hilbert spaces and other function spaces, and are based on previous results in Chichilnisky (1977, 1981).