A Unified Approach to Market Incompleteness

Abstract

We introduce a general class of incomplete markets that includes almost all well known examples of market incompleteness in finance and macroeconomics. Two concrete examples are the problem of idiosyncratic income shocks and general, diffusion driven incompleteness. For all markets in this class we explicitly solve the associated utility maximization problem by a recursive construction and derive many important properties. For example, precautionary savings and the diminishing marginal propensity to consume. Effectively, the class is characterized by these two economic properties. We also prove that the growth rate of consumption is always larger when markets are incomplete and that precautionary savings are monotone increasing in the size of idiosyncratic risk. Our construction can be implemented computationally by an efficient, robust numerical scheme.

Keywords: incomplete markets, idiosyncratic risk, precautionary saving, investment, marginal propensity to consume

JEL Classification: G11, E21, D91, D81