Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics

Professor G.L. Kulinich (09.12.1938 – 10.02.2022) – prominent scientist and teacher

Fri, 09 Dec 2022 00:00:00 +0200

Pages of the article in the issue: 11 - 21

Language of the article: Ukrainian

Invariant surfaces for certain classes of systems of the second-order to stochastic diﬀerential equations with jumps

Yu. S. Mishura, S. V. Kushnirenko, L. V. Voloh — Fri, 09 Dec 2022 00:00:00 +0200

In this paper, we consider the concept of invariant sets of inhomogeneous stochastic diﬀerential equations with jumps. For certain classes of systems of the second order of inhomogeneous stochastic diﬀerential equations with jumps the necessary and suﬃcient conditions for the invariance of the corresponding surfaces are established. The obtained results provide opportunities to ﬁnd the invariant surfaces and conditions of their invariance for the speciﬁed classes of stochastic diﬀerential equations.

Pages of the article in the issue: 22 - 27

Language of the article: Ukrainian

Mathematical model of financial dynamics of an insurance company

V. P. Zubchenko, A. V. Tkachenko — Fri, 09 Dec 2022 00:00:00 +0200

This paper is devoted to the construction of a mathematical model of financial dynamics of life insurance company. The methods of calculating insurance amounts, payments, net premium reserve are studied, their generalization is carried out taking into account various types of insurer's expenses for ensuring the activities of the insurance company, the sensitivity of the financial dynamics of the insurance company depending on the input parameters of the model is analyzed. The results of the work are of great practical importance for modeling the work of the insurance company, because the National Bank of Ukraine implements mandatory monitoring of the solvency of the insurance company on the basis of the insurer's reporting data.

Pages of the article in the issue: 28 - 36

Language of the article: Ukrainian

Study of the dynamics of the interest rate swap using machine learning methods

V. P. Zubchenko, P. V. Aleksandrova — Fri, 09 Dec 2022 00:00:00 +0200

For the European ﬁnancial system, the interest rate swap is a well-known mechanism to reduce the potential eﬀects of these risks, but it is new to the Ukrainian interbank market. In the second half of 2020, the National Bank of Ukraine and commercial banks held their ﬁrst interest rate swap auctions. According to this provision, one party oﬀers the other a ﬂoating interest rate while the other oﬀers a ﬁxed interest rate based on a conditional amount. Based on the Ukrainian overnight interbank rate index, the latter is computed (UONIA). Future cash ﬂows are discounted at rates determined by the zero coupon yield curve created for hryvnia government bonds. The parties agree on how to calculate the diﬀerence in interest payments within the predetermined period of time. The analysis of the fair value of this ﬁnancial instrument at future points in time is the main concern of mathematical modeling of interest rate swap transactions. Predicting future changes in fair value is particularly crucial when the zero coupon yield curve’s coeﬃcients vary and when there are speciﬁc trends in the index of overnight interbank rates. The sensitivity of the speciﬁed factors to the interest rate swap’s dynamics was investigated in the study, and a forecast of the instrument’s future dynamics based on the change in important macroeconomic indicators was developed.

Pages of the article in the issue: 37 - 41

Language of the article: Ukrainian

Corepresentations of Munn matrix algebras

V. M. Bondarenko — Fri, 09 Dec 2022 00:00:00 +0200

Let A be an algebra over a field K, m and n natural numbers and P = (p_j_i) a fixed n x m matrix over A. The K-vector space of all m x n matrices over the algebra A can be made into an algebra with respect to the following operation (o): B o C = BPC. This algebra is called the Munn matrix algebra over A with sandwich matrix P. The algebras of such type arose as generalizations of semigroup algebras of Rees matrix semigroups which in turn are closely related to simple semigroups.

This article describes the generators and defining relations of Mann matrix algebras with a regular sandwich matrix.

Pages of the article in the issue: 42 - 44

Language of the article: English

Method of identification of atomic elements of information space with the help of a unified information space

Iryna Zamrii, Viktor Vyshnivskyi — Fri, 09 Dec 2022 00:00:00 +0200

The article considers a method that allows to identify the input atomic element of the information space by combining information spaces into a unified information space (this is an information model of a complex subject area, which includes information objects, relationships between them, space environment and processes). This method allows you to refine the missing features for the input element to enable it to be added to a unified information space.

Pages of the article in the issue: 47 - 54

Language of the article: Ukrainian

A intellectual system of analysis of reactions to news based on data from Telegram channels

Fri, 09 Dec 2022 00:00:00 +0200

This paper describes the system of intellectual analysis and prediction of reactions to the news based on data from Telegram channels In particular, the features of collecting and pre-processing datasets for the intelligence systems, the methodology of thematic analysis of the received data, and the model used to obtain predictions of reactions to Telegram messages depending on their text are described We show the work of this system in the example of the Ukrainian news Telegram channel The results are estimations of probability of emojis for the news from the testing dataset Also, we give F-measures for our approaches to precise input data and models.

Pages of the article in the issue: 55 - 61

Language of the article: Ukrainian