the method of calculation of natural disasters lie in the use of average values, hos located using Pareto for calculation of damage described by the exponential by law, taking into account the growth of the expected damage over time.

Statistically optimal algorithm for finding minimal cover of 0.1-matrices for the unweighted matrix has been proposed in the works of O. V. German. The algorithm is based on iterative addition of new columns (columns-resolvent)to the matrix, which are built according to the authors' formulated the principle of group resolution (PGR). They have the following property. Under the assumption that optimal cover has not been obtained yet, each such cover contains at least one row from among those that cover the column - resolvent. After adding each new column, considered as a random 0.1-vector, analytical evaluation of mathematical expectation of the number of minimal covers with a given number of rows is made. The evaluation concludes the need to continue the iterations or termination of the algorithm. After evaluation it can be concluded about the necessity to continue the iterations or termination of the algorithm.The algorithm is tested for 600 randomly generated problems with a subsequent comparison with the exact solution. It can be concluded that analytical estimates for mathematical expectation of the number of covers with specified size are stable for matrices of large dimension. On the contrary, with a decrease in the number of columns these estimates become less stable. Doubtless, in our opinion, advantage of this method is its high speed. Thus, in the vast majority of cases, the algorithm concludes by finding the exact solution, which makes to consider it statistically optimal one. The advantage of this method is its speed, but it is empirically proven that increase in the dimension of the problem leads to unpredictable failures.

The paper presents studies of linear models of economic dynamics of the Neumann-Gale type, taking into account their possible stationarity, presents an analysis of existing classification approaches to the concept of optimality, presents their advantages and comparative characteristics, it is noted that the first type model - open - connects the concept of optimality with discounted maximization total utility. The first considers a closed system, the technological description of which includes the reproduction of all the resources necessary for development, including labor. Such a system has no external goals; its natural end in itself is development at the maximum pace. This is the most abstract and idealized scheme, but on the other hand it was it that made it possible to develop such fundamental concepts as equilibrium, a ray of (Neumann) balanced growth. Later, the apparatus of the closed model was replenished with the concepts of “direct and inverse Bellman operators”, “effective functional” (“potential”) of the model, etc. The second approach involves explicit accounting for consumption. Here the description becomes open, consumption is derived from the "technology" and described using the utility function. A new approach to the concept of “optimal development strategy” is proposed, a detailed analysis of the corresponding model is given. The article consists of three sections. 1 - staging part; 2 - analysis of the model with illustrative examples; 3 - conjugate (dual) model. The last section contains the main result on the connection of the optimal trajectories of the direct and dual problems. The paper provides an overview of literary sources in the subject area, as well as an economic interpretation of the results.