Optimal consumption/investment policies with undiversi"able income risk and liquidity constraints

This paper examines the continuous time optimal consumption and portfolio choice of an investor having an initial wealth endowment and an uncertain stream of income from non-traded assets. The income stream is not spanned by traded assets and the investor is not allowed to borrow against future income, so the "nancial market is incomplete. We solve the corresponding stochastic control problem numerically with the Markov chain approximation method, prove convergence of the method, and study the optimal policies. In particular, we "nd that the implicit value the agent attaches to an uncertain income stream typically is much smaller in this incomplete market than it is in the otherwise identical complete market. Our results suggest that this is mainly due to the presence of liquidity constraints. ( 2000 Elsevier Science B.V. All rights reserved. JEL classixcation: C61; G11