Alternative measures of risk of extreme events in decision trees

A need for a methodology to control the extreme events, defined as low-probability, high-consequence incidents, in sequential decisions is identified. A variety of alternative and complementary measures of the risk of extreme events are examined for their usability as objective functions in sequential decisions, represented as single- or multiple-objective decision trees. Earlier work had addressed difficulties, related to non-separability, with the minimization of some measures of the risk of extreme events in sequential decisions. In an extension of these results, it is shown how some non-separable measures of the risk of extreme events can be interpreted in terms of separable constituents of risk, thereby enabling a wider class of measures of the risk of extreme events to be handled in a straightforward manner in a decision tree. Also for extreme events, results are given to enable minimax- and Hurwicz-criterion analyses in decision trees. An example demonstrates the incorporation of different measures of the risk of extreme events in a multi-objective decision tree. Conceptual formulations for optimizing non-separable measures of the risk of extreme events are identified as an important area for future investigation.