Portfolio and consumption decisions with the consumption habit constraints

Abstract

In this paper we first argue that for a large group of investors, their portfolio and consumption choice problem must be attached to a consumption habit constraint. By using the Cox and Huang martingale approach, we obtain the optimal consumption behavior for the consumption habit. For the investors who adopt some special forms of the consumption habit, we study their investment behavior. For the constant relative risk aversion (CRRA) based investors, their behavior is related to the constant proportion portfolio insurance (CPPI) investment strategy. The deterministic part of the consumption habit will reduce the demand for risky assets and the stochastic part will increase the demand for risky assets. Once imposing the consumption habit requirement, even for the CRRA utility, the demand for risky assets is not myopic in the Merton's (1973) definition any more.