Portfolio and Consumption Decisions with Consumption Habit Constraints

In this paper we first argue that for a large group of investors, their portfolio and consumption choice problem must be attached a consumption habit constraint. For this new choice problem, by using the Cox amp; Huang martingale approach, we obtain optimal consumption behavior for general consumption habit. For some special consumption habit we study the investment behavior of the investor. For the CRRA (Constant Relative Risk Aversion) investor, the behavior of the investor is related with CPPI (Constant Proportion Portfolio Insurance). Certain part of the consumption habit will decrease the demand for risky assets and stochastic part will increase the demand for risky assets. After imposing the consumption habit requirement, even for the CRRA utility, the investor's demand for risky asset is not myopic any more