  We demonstrate a limitation of discounted expected utility, a standard
approach for representing the preference to risk when future cost is
discounted. Specifically, we provide an example of the preference of a decision
maker that appears to be rational but cannot be represented with any discounted
expected utility. A straightforward modification to discounted expected utility
leads to inconsistent decision making over time. We will show that an iterated
risk measure can represent the preference that cannot be represented by any
discounted expected utility and that the decisions based on the iterated risk
measure are consistent over time.
