Abstract: This article incorporates an illiquid asset in theframe of Merton's classic theory on intertemporal optimal consumption and portfolio selection. In this paper we develop a 3-asset finite-horizon continuous time model to explore impacts of illiquidity on the restricted investor's optimal consumption and invest ment decisions. An analytical solution is given using the standard dynamic programming approach. The numerical analysis demonstrates that the true value of the illiquid asset to the investor is less than its mar ket value, and the shadow price is needed to reflect this liquidity effect. Moreover, the liquidity constraint decreases the investor's welfare and affects his consumption and investment strategies significantly.

Key words: illiquidity, intertemporal optimization, dynamic programming, shadow price