The project will develop the theoretical foundation for the integration of statistics of extremes, the conditional - low probability/high consequences - risk function f4, and the generalized concept of return period for the management of extreme natural events such as rare floods. Four tasks will be undertaken: a) sensitivity analysis of risk functions associated with extremes; b) classification of Gumbel types for various risk functions; c) the application of distribution-free results to dam-safety problems; and d) trade-off analysis in risk management based on multiple risk information. The results will have wide application to the mitigation of natural hazards impacts.