Multi-period consumption and investment decisions under uncertainty revisited

This paper studies the consumption-investment problem of a consumer with a multi-period planning horizon under uncertainty. Such a setting occurs naturally in stochastic OLG models with multi-period-lived consumers. We provide a rigorous characterization of consumption-investment strategies under general assumptions on preferences and expectations and derive conditions for the existence of an optimal strategy. The properties of the resulting demand functions are investigated in general as well as for the popular case with constant relative risk aversion (CRRA).