An ultra-fuzzy model of aggregate growth in catastrophic risk potentials

Catastrophic loss potentials are characterized by very low probabilities of devastating (irreversible) damages. As a result of the complexities inherent in such exposures, and the limited availability of data, considerable uncertainties enter into their estimation and treatment. The difficulties increase when we consider the aggregation of such loss potentials. We suggest here that the growth of catastrophic loss potentials can be modeled using ultra-fuzzy sets, which capture the wide uncertainties involved. The ultra-fuzzy model has important implications for the way we manage high-stakes risks.