Discrete-Time Optimization of Consumption and Investment Decisions Given Intolerance for a Decline in Standard of Living

Abstract

We extend Samuelson's (1969) discrete-time dynamic consumption and investment optimization problem to the case where the investor is intolerant of any decline in her standard of living. This constraint represents a strong form of habit formation such that the consumption rate is non-decreasing over time. To achieve this objective, the investor first guarantees a consumption perpetuity at the current consumption rate and then allocates the remaining wealth under a state-dependent, adjusted coefficient of relative risk aversion. We study the impact of the length of the time interval on the optimal consumption and investment policies. This effect has implications for investors considering investments in assets, such as hedge funds and private equity, that have restrictions on trading intervals.

Keywords: consumption-portfolio choice, habit formation, alternative investments, hedge funds, stochastic dynamic programming

JEL Classification: C61, E21, G11, G23, H30