The work is devoted to the study of the structure of the universal set of abstract risks of the development of discrete economic systems under conditions of probabilistic uncertainty from a set-theoretic point of view, as well as the formulation of a number of related problems. In particular, the article shows a trivial characterization of a universal set of abstract risks in the form of an isomorphism of the corresponding factor monoid with the operation of calculating the joint risk of a monoid of integers by multiplication. Using the methods of information theory, the components of dividing the risk space, which form a subtler, in relation to the named isomorphism, characterization of the universal set of risks, are investigated. The relevance of entropy approaches to risk analysis is shown. The problem of risk factorization, interesting from the point of view of system analysis, is formulated. Formal statements of factorization problems are given.