Catastrophic risk: indication, quantitative assessment and management of rare extreme events using a non-expected utility framework

Abstract

The paper develops a conceptual framework for the analysis and management of catastrophic risk. The framework serves to assess rare extreme events in systematic, quantitative and consistent ways. It dispenses with probabilistic extreme value theory, concentrating on descriptive statistics and simple probability distributions. Risk assessment is based on a recently developed axiomatic approach to non-expected utility preferences defined on the set of risky alternative courses of action available to an agent. The utility values of catastrophic risks are given an explicit algebraic representation, which shows them to be highly unstable (“elastic”) in the sense that they respond disproportionately to small perturbations of the decision outcomes and their probabilities. Various elasticity coefficients are defined for the outcome variables and utility preferences attached to them. They indicate whether a variable possibly takes on large negative values. The coefficients can also be defined as sample statistics and, thus, computed from observed data. The approach admits various applications to practical problems of disaster risk management. The applications include estimations of the effectiveness and cost-efficiency of risk management, the specification of limits of acceptance of catastrophic risk for regulatory purposes, and safety and security systems design and dimensioning.