Optimal Consumption/Investment Policies with Undiversifiable Income Risk and Borrowing Constraints

We examine the 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 financial market is incomplete. We solve the corresponding stochastic control problem numerically with the Markov chain approximation method. In particular, we find that the implicit value, the agent attaches to an uncertain income stream, can be much smaller in this incomplete market than it is in the complete market.