Economics and Mathematical Methods

This article analyzes the dependence of stock index dynamics on two types of factors — objective and subjective — which are understood, on the one hand, the dynamics of economic development, and, on the other hand, the activities of various stock market participants, affecting both the dynamics of the entire stock market and the values of stock indices. At the beginning of the article, the structure of the ratios of these factors is considered, and a summary of the content of the article is given. It is assumed that the main trend in the dynamics of the stock index, represented by the regression model, characterizes the results of objective factors, and deviations from it — subjective factors. After reviewing the works devoted to the construction of regression models for various stock indexes, a brief description of the history of the creation of the most famous stock index, the Dow–Jones index, is given. Based on the dynamics of this index for 1897–2024, regression models describing its main trend are built and the deviations of the index from this trend are analyzed. It is assumed that this trend depends on the objective characteristics of economic development, and deviations from it depend on the influence of subjective factors. It is shown that the main reasons for these deviations are incorrect time and intensity changes in the list of companies for which it is calculated, made by the managers of the index. This is interpreted as the influence of such a subjective factor as the “human factor” on the dynamics of this index. The level and significance of these deviations are further assessed against the background of the dynamics of US GDP, and it is shown that although in some periods of time the “human factor” deviates the dynamics of the index from the dynamics of US GDP, in general, the dynamics of the US economy has some “attractive force” for the dynamics of the Dow–Jones index. In conclusion, it is noted that when constructing models of stock indices, it is necessary to take into account the specific features of their structure, including the principles of changing their lists, the role of coefficients in the formulas for calculating these indices, and their other characteristics.

The current stage of development of the Russian economy is accompanied by fundamental changes in the innovation sphere. The processes of obtaining new knowledge and technologies and their effective use to improve the level of socio-economic development of the country largely determine its significance and place on the world stage and play an important role in ensuring national security. However, at the stage of technical preparation for the implementation of innovative projects, not all entities and not always can correctly determine the potential prospects and dynamics of transformations. This indicates the relevance of the topic of scientific research. The current practice of organizing technical preparation of innovative projects is often accompanied by various kinds of errors. The most significant of them are associated with incorrect estimates of the timing of individual stages of the project, a low level of communication between its potential participants and insufficient elaboration of various options for its implementation. The consequence of this state of affairs is obviously incorrect estimates of the dynamics of external and internal environmental factors, insufficient consideration of the physical and cost volumes of material and technical support, a low level of preparation of pre-project and project justifications for the implementation of innovative projects. These and a number of other circumstances entail a decrease in the effectiveness of investments in the innovative sector of the real economy. The authors believe that the use of probabilistic planning methods will increase the level of interaction between all investors and performers, and will also help to better assess innovation risks taking into account the project implementation timeframes. It is proposed to make a decision on choosing a project option for its further implementation using probabilistic planning and game theory methods.

In this work, hedonic indices and hedonic regressions are estimated for smartphone prices. The indices are built using a special collection of big data from online retailers that comprises a large number of representative observations and a wide range of product attributes (1.9 million distinct smartphone price observations since July 2022). We demonstrate that, for smartphones, the dynamics of hedonic indices built with the techniques suggested in the literature are substantially greater than Rosstat price index. Furthermore, we indirectly validate that the skimming pricing strategy of smartphones, in which a high price is initially set for a variety and then lowered. In the case of using simple methods of accounting for quality in the consumer price index, that is common among statistical agencies, the use of pricing strategies by manufacturers and retailers, along with frequent changes in product ranges, ultimately result in the depletion of the observation sample and a bias in the consumer price index. This supports the use of hedonic regression-based techniques to enhance the ways in which price dynamics are adjusted for changes in quality. Hedonic regressions should use all quality attributes that are pertinent to price fluctuations as regressors rather than fixed effects of varieties, according to another finding. A bias in the consumer price index happens when simplified regression specifications are used. For price adjustments, Rosstat will be encouraged to collect information on all qualitative traits of the varieties. Increased confidence in the published data will result from the addition of hedonic methods to Rosstat’s toolkit, which will help make the published CPI more representative.

The topological model presented in this article is a tool for the economic and mathematical analysis of diversification processes in enterprises of the military-industrial complex carried out by “Rosatom” State Corporation. Based on an analytical review of scientific literature, the most pressing issues of diversification of defense industry enterprises were identified. The lack of a theoretical and normative-methodological framework for studying transformation processes is noted. Critical analysis of the methodology governing the activities of defense enterprises revealed shortcomings such as a standardized approach to diversification, a predominance of quantitative indicators, and the absence of adequate indicators to reflect economic feasibility. The existing problems can be eliminated mainly by using the topological model described in the article. Its development was based on conditional data that was structurally close to real information on a representative sample of enterprises, including scientific, scientific-production, and production organizations. Based on this model, seven categories of enterprises were identified, characterized by similar patterns in the transformation processes under consideration. Within the model framework, the joint changes in performance indicators and the levels of diversification of these groups of enterprises were investigated, and their dynamic stability was analyzed by comparing the identified patterns for two time periods (2018–2020 and 2021–2023). This work demonstrates graphs showing the topological areas obtained for the identified categories of companies. Numerical boundaries for these topological objects are also provided. The results obtained substantiate the conclusion that a differentiated approach to the problems of transforming the industry in question is necessary and can also be recommended for improving methodological provisions governing the planning processes of diversification at “Rosatom” State Corporation enterprises.

We consider machines used in the production process of an enterprise, the failure of which leads to a stoppage of this process and losses. The technical condition and operating characteristics of machines deteriorate with an increase in their operating time. We construct a model for determining the optimal service life of such machines, which assumes that a failed machine is disposed and immediately replaced with a new machine of the same brand. However, the replacement process usually requires random, sometimes quite a long time. Then it is advisable to use a backup machine, and the subject of consideration is a complex of interchangeable main (working) and backup machines of the same brand. In this case, losses from stopping the production of the enterprise arise only after the failure of both machines of the complex, when orders for the delivery of replacement new machines is not yet been fulfilled. Methods of reliability theory and general principles of valuation theory allow us to construct a model for solving the problem of optimal control of the specified complex in discrete time. It turns out that decisions on decommissioning of one machine of the complex, on its designation as the main or backup machine should be made depending on the existence and condition of the second machine. The calculations carried out allow us to assume that of the two machines in the complex, the machine with the lower operating time should be designated as the main one, however, it is not possible to prove the validity of this hypothesis.

The development of distributed ledger technologies (blockchain) led to the alternative ways to finance projects based on the issuance of tokens — digital accounting units in blockchain platforms. Unlike traditional financing mechanisms, the use of tokens allows for greater flexibility in fundraising and income and management rights allocation among stakeholders. An urgent problem that arises when using this mechanism is to determine the proportions in which tokens are distributed among the stakeholders of the project. Currently, this problem is solved by each project individually, based on its organizers’ subjective vision. In the article, the problem of token allocation of a decentralized project is investigated from the point of view of cooperative game theory. A token allocation model is considered in the form of a three-party cooperative game and the properties of its solutions are investigated, based on the core, Shapley value and nucleolus. The model allows to obtain estimates of rational token allocations corresponding to the participants’ contributions in the project, as well as stable to individual parties and their coalitions deviations. It also makes possible to solve the inverse problem of assessing the contribution of participants and their coalitions to the value of the project based on information about the past token allocation.