A body of empirical evidence has shown that many managers would welcome new ways of highlighting catastrophic consequences, as well as means to evaluating decision situations involving high risks. When events occur frequently and their consequences are not severe, it is relatively simple to calculate the risk exposure of an organisation, as well as a reasonable premium when an insurance transaction is made. The usual methods rely on variations of the principle of maximising the expected utility (PMEU). When, on the other hand, the frequency of damages is low, the situation is considerably more difficult, especially if catastrophic events occur. When the quality of estimates is poor, e.g., when evaluating low-probability/high-consequence risks, the customary use of quantitative rules together with overprecise data could be harmful as well as misleading. This work extends the risk evaluation process by the integration of procedures for handling vague and numerically imprecise probabilities and utilities. The shortcomings of PMEU, and of utility theory in general, can in part be compensated for by the introduction of risk constraints. We point out some problematic features of the evaluations performed using utility theory. We also criticise the demand for precise data in situations where none is available. As an alternative to traditional models, we suggest a method for the evaluation of risks when the information at hand is numerically imprecise. The method includes procedures that allow for interval statements and comparisons, and thereby it does not require the use of numerically precise statements of probability, cost, or utility in a general sense. In order to attain a reasonable level of security, and because it has been shown that managers tend to focus on large negative losses, it is argued that a risk constraint should be imposed on the analysis. The strategies are evaluated relative to a set of such constraints considering how risky the strategies are.
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