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    <abstract>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.</abstract>
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