Staying the Course or Rolling the Dice: Time Horizon’s Effect on the Propensity to Take Risk

This paper analyzes a model of dynamic decision making under uncertainty, where in each period the decision maker (DM) is faced with a choice between accepting a known level of benefit inherited from the last period (“staying the course”) and drawing from a random benefit distribution (“rolling the dice”). It shows that the DM’s propensity to roll the dice decreases as it gets closer to the ending period, therefore providing a justification for the conventional wisdom that the young would take more risk than the old. Other results are also derived and compared with those from the standard model of decision making under uncertainty. These include that it is possible for a risk averse DM with an inherited benefit level greater than the mean of the random benefit distribution to prefer rolling the dice to staying the course, and that it is also possible for a risk averse DM to be more prone to risk taking as the underlying benefit distribution becomes riskier.