Calculation of Discrete Risks in Conditions of Probabilistic Uncertainty

The paper shows a model for abstract risks calculation of the evolution of systems of arbitrary nature with a discrete set of states under conditions of probabilistic uncertainty. We deal with algebraic structures arising on a universal set of abstract risks and their parts. We formulate an analogue of the polynomial theorem on this set, which takes place under the condition of commutativity of evolutionary transformations of the state of the system. We give a number of natural congruence relation on a universal set of abstract risks and their parts, which also make it possible to increase the efficiency of calculations in practice.