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**:** 2020
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**:** 88
**:** .. , // . 88. .: , 2020. .41-68. DOI: https://doi.org/10.25728/ubs.2020.88.3

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** (.):** decision-making under risk, the maximal guaranteed result, the quantity of information

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** (.):** It is well known that for effective management it is necessary to use information about the surrounding world. But if there is a lot of this information, then one have to save the resources spent on its receipt and processing. Therefore, the question arises of finding rational ways to handle this information. One of the models that allow us to study this question by formal methods is investigated in the article. The simplest control system under risk is considered. It is assumed that information about the realized value of a random factor is available to the operating party. This information is encoded in binary words. The choice of information content, that is, the encoding method, is considered as the prerogative of the operating party. A control result acceptable to the operating party is determined. The task is set to find an encoding method that can guarantee to get this result with the smallest expected value of the length of the message about the realized value of the uncertain factor. It is shown that under very general assumptions this expected value is finite. The qualitative structure of the function from the set of possible values ?of a random factor to the set of binary words, which defines the optimal coding method, is clarified. The task of search such a function is reduced to solving the stochastic programming problem on a finite-dimensional space. The results obtained have a reasonable meaningful interpretation. This allows us to conclude that the model constructed correctly reflects the main features of the simulated phenomenon and deserves further study.

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