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Risk of crisis phenomena in regions emphasizes the importance to build the system of continuous monitoring for analysis and assessment of the threat level for socioeconomic security. There is the need for carrying out continuous monitoring of all reproduction socioeconomic processes state: the process of production, the cash outflow and the flow of return, the variation level of prosperity. As the basis of the system of complex monitoring, there should be used formalized algorithms on the basis of mathematical models with the use of all available data including those for specification and assessment of socioeconomic relationships rather than a traditional intuitive analysis and expert methods. The level of development of modern equipment and mathematical support allows to process the huge collections of data which the researchers of previous generations did not have. Extremum modelling is a complex area. The data on emergency situations are poor by definition, and forecasts and estimates should be often made on the brink or even beyond available data. Thus, there is the need to create the theory of risk management connected with catastrophic events.