Savings and Consumption with an Uncertain Horizon

Abstract

This paper studies the effect of lifetime uncertainty on optimal consumption decisions. It is shown that for risk averters changing the distribution of lifetime uncertainty decreases consumption due to the higher probability of having a longer life and increases consumption due to the desire for sure consumption in the present. The stronger of these effects determines the effect of lifetime uncertainty on optimal consumption decisions. The major result is that if the utility function is Cobb-Douglas and the rate of return is not too large relative to the amount of future discounting then lifetime uncertainty will always increase consumption.