Catastrophic Risk Evaluation. Love Ekenberg, IIASA, International Institute for Applied Systems Analysis, A-2361 Laxenburg, Austria; Magnus Boman, Department of Computer and Systems Sciences, Stockholm University, Electrum 230, S- 164 40 Kista, Sweden; and Joanne Linnerooth-Bayer, IIASA, International Institute for Applied Systems Analysis, A-2361 Laxenburg, Austria
A variety of methods have been developed for estimating losses and risks. When events occur frequently and when they are not very severe, it is relatively simple to calculate the risk exposure of an organisation, as well as a reasonable premium when, for instance, 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; in particular, if catastrophic events can occur. When the quality of the estimates is poor, i.e. when evaluating low-probability/high-consequence risks, the ordinary use of quantitative rules together with precise information could be harmful as well as misleading.
It has often been argued that various axiomatic theories proposed to support PMEU are too strong. It has also been demonstrated that several axiom systems are too weak to imply the principle and that it seems very hard to design such a system. Therefore, it seems necessary to supplement the PMEU by other criteria. While a certain evaluation of a strategy may result in an acceptable expected utility, some consequences of adopting it might be so serious that it should nevertheless be avoided, and in that case even if the probability of catastrophic events is low.
In this paper 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 does not require the use of numerically precise statements of probability, utility, and cost. In order to attain a high level of security it is argued that security constraints should be imposed on the analysis. The strategies are evaluated relative to a set of such constraints considering how risky the strategies are. Moreover, we investigate in which parts of the solution space those conditions are met. This is accomplished by introducing contractions into the framework.
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