This paper studies the consumption, labor and asset allocation problem of an agent, who is liquidity constrained and faces a stochastic wage that cannot be spanned by the available financial assets. The market is, as a result, incomplete. I also allow for simple trade restrictions which further increase the incompleteness of the economy. The optimal controls and the value function are characterized in terms of the viscosity solution of the associated Hamilton-Jacobi-Bellman equation, which is shown to exist and is characterized. The paper also shows that under a parameter restriction the viscosity solution is unique and for certain levels of risk aversion it is sufficiently smooth and coinciding with the classical solution which as a result exist and is unique. In addition the paper studies how the value function, consumption, labor and portfolio policies depend on the wealth to wage ratio. In particular it is shown that the wealth equivalent implicit value of the lifetime maximal wage income is increasing in the wealth to wage ratio and that for high wealth to wage ratios the agent will choose not to work. Finally the paper shows that the value function, the optimal consumption and the optimal portfolio weights approach the value function, the optimal consumption and the optimal portfolio weights respectively in a Merton (1969) setting without a labor-leisure choice, as the wealth to wage ratio goes to infinite.