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Background: Some firms with good growth opportunities and additional funds could have difficulties accessing external finance. One possible way to enhance their financial inclusion could be an exciting approach to planning the money reserve collected on a firm's account. Methods: This article aims to disclose the introduction of financial logistics as the new theoretical field of management science. The authors present, in this paper, the key findings on the development of logistical models of an optimum money reserve calculation taking into account digital transformation and industry 4.0 technologies and optimization methods. Results: The monetary reserve models are analogies of models of storekeeping in supply chains. The specific area of the theoretical research of logistics is shown in this paper, which could be disclosed as the subject of financial logistics as a science. The authors consider the term \"Financial Logistics\" based on logistics theory and money demand. Conclusions: Authors suggest the methodology of studying the nature of both financial and material flows of resources by comparing the relevant formulas. From the researchers' points of view, financial logistics could be defined as the theory of managing the cash flows based on the logistical models for calculating a corporation's cash reserve. The authors find it interesting to expand the conditions for calculating financial flows since the uncertainty of external market conditions always influences actual commercial activity.

The development of conceptual models of a digital city poses numerous challenges for developers. The public sector concept model has become one of the most difficult models to use. When developing algorithms to find a solution, the multidirectional interests of businesses and public institutions are combined. This type of model reflects the most acute and urgent problems faced by megapolises with regard to combining numerous localized services provided to the community in a limited territory. The administrations of both cities and regions (the scale of the smart territories) must make decisions concerning overcoming the barriers existing between the profits of commercial structures, the negative externalities generated by their activities, and the social benefits to the population in the territory under their control. It is necessary to solve this problem to achieve the effective management of enterprises belonging to the segment of long-term participants in various business activities, interacting with the surrounding social and business environment in a complex. This study takes into account the complex structures of the economic processes characteristic of megacities. The periodicity of economic processes is also taken into account. When choosing an optimization criterion, functions reflecting the level of internalization of responsibility for external effects were considered. The authors propose a mathematical model that can be used as part of the management decision support systems software, aiming at taking into account the externalities of a wide range of national, institutional, business, and social activities.

The Volatility Index (VIX) is a real-time index that has been used as the first measure to quantify market expectations for volatility, which affects the financial market as a main actor of the overall economy that is sensitive to the environmental and social aspects of investors and companies. The VIX is calculated using option prices for the S&P 500 Index (SPX) and is expressed as a percentage. Taking into account that VIX only shows the implicit volatility of the S&P 500 for the next 30 days, the authors develop a model for a near-optimal state trying to avoid uncertainty and insufficient accuracy. The researchers are trying to make a contribution to the theory of socially responsible portfolio management. The developed approach allows potential investments to make decisions regarding such important topics as ethical investing, performance analysis, as well as sustainable investment strategies. The approach of this research allows to use deep probabilistic convolutional neural networks based on conditional variance as a linear function of errors with the aim of estimating and predicting the VIX. For this purpose, the use of technical indicators and economic indexes such as Chicago Board Options Exchange (CBOE) VIX and S&P 500 is considered. The results of estimating and predicting the VIX with the proposed method indicate high precision and create a certainty in modeling to achieve the goals.

Nowadays, digitizing the data stream is enabling the evolution of logistics processes. The data-driven network logistics processes are evaluated by leading economic indicators. The purpose of this study is to further develop the algorithmic foundations of economic and mathematical modeling of logistics networks based on advanced technologies that the digitalization process provides. Methods of mathematical modeling of flows of various resources in logistic networks, the structure of which is presented in the form of a graph, are used in the work. The economic benefit lies in the implementation of the planning concept based on leading indicators. As a result, using a set of formalisms, a mathematical model has been developed, which will make it possible to search for optimal solutions based on the criterion of economic efficiency. The results obtained will find application not only in transport problems. Network logistics includes the transportation of liquid and gaseous materials through pipelines, energy through electrical networks. A universal mathematical model will allow the results to be applied in many industries and economic activities when it is required to make economically sound decisions based on a stream of digital data coming in real time.

Background: The ongoing COVID-19 quarantine restrictions have caused multiple sharp decreases in activities associated with the movement of large masses of people. The economies of regions and cities that are critically dependent on tourist flows related to various segments have suffered. This research aims to provide an economic-mathematical model of smart cities externalities' impact from the point of view of achieving social and environmental goals Methods: The objective of this study was to develop an algorithm for supporting decision-makers. Methods of mathematical modeling, statistical processing of data received in real-time, as well as methods for finding solutions by expansion into dynamic series are used, and the theory of mathematical games is applied. The theoretical mathematical model presented considers the statistical processing of data provided in real time referring to the performance indicators of megacities. Results: The activities of administrations and governments aimed at maintaining stability over the past two years have been aimed at reducing the negative impact of the pandemic. The prospect of returning to normal conditions is complicated by a number of factors. The proposed approach allows the development of the fundamental basis for making administrative decisions within individual megapolises and in environmental policy on a territory of any scale. The developed mathematical model is abstract by definition and is applied by taking into account specific tasks and criteria. Since the tasks of the administration differ depending on the region and country, the choice of criteria is set individually. Conclusions: During the period of isolation, the volume of services in the Hotel - Restaurant- Catering/Café (HORECA) segment has decreased, and personnel has also been lost. The reduced pressure on public infrastructure and the departure of migrants means that, in the long term, this work cannot be restored within a short period of time.

The purpose of the study is to test the role of energy development in energy financing considerations for sustainable energy innovation and financial development. To achieve the study objective, a fuzzy decision-making modeling technique is applied. The results revealed that bank loans are now the main source of financing for innovation and creativity in Chinese business entities. Project-based financing might be replaced with collaborative and sustainable energy innovation (CSI), warranting energy development. Moreover, green financing loan schemes invest both public and private funds in sustainable energy innovation to capitalize on financial development through sustainable energy innovation. The consideration and application of financial consideration for sustainable energy innovation-financing projects or companies are limitless. Providing for screening energy development cooperation proposals with small financial payback hurdle rates might have large opportunity costs. There may be a case for governments to increase industrial growth, improve resource efficiency, and increase factor productivity while tackling climate change. Economic growth in China may have an even greater influence on environmental sustainability than in other countries. On such points, there is a need to pay the attention. If the suggested policy suggestions are implemented successfully, they would help to enhance the scope of financing considerations for sustainable energy innovation to uplift financial development through energy development mechanisms at the corporate level.

The development of modern logistics systems requires state-of-the-art solutions for simultaneously achieving sustainable development goals and ambitious business targets. On this issue, the challenge of implementing digital technologies in social life, in particular in smart cities, deserves special attention. The diversified application of Industry 4.0 doctrine and digital shadow penetration to all fields of socioeconomic systems highlights the gaps in the design, control, and efficiency assessment of digital tools in the logistics of smart cities. Another challenge concerns the need to consider environmental, social, and governance (ESG) principles amid the deployment of harmonic digital tools within urban territories. All these issues require a complex methodological approach toward understanding the role of IT in the modern economy through an ESG prism. The article contains a contemporary literature review on the related topic and the conceptual framework of city logistics digitalization under ESG perspectives and constraints. The mathematical model proposed by the researchers enables a multidimensional design of digital solution applications within smart city logistics performance. The designed discrete stochastic model is eligible for scaling toward and the further development of variables other than the key ones mentioned above. The mathematical formalization of the proposed model considers the distribution of the limited budgeting of administrative branches within city logistics, highlighting the research relevance in connection with the ESG principles.

Globalization has given a powerful impetus to the development of international commercial activity and logistics management systems taking full advantage of cross-border networking. The solution lies at the intersection of information technologies, technical means of machine-to-machine (M2M) interaction, mobile high-speed networks, geolocation, cloud services, and a number of international standards. The current trend towards creating digital logistics platforms has set a number of serious challenges for developers. The most important requirement is the condition of sustainability of the obtained solutions with respect to disturbances in the conditions of logistics activities caused not only by market uncertainty but also by a whole set of unfavorable factors accompanying the transportation process. Within the framework of the presented research, the problem of obtaining the conditions for the stability of solutions obtained on the basis of mathematical models is set. At the same time, the processes of transferring not only discrete but also continuous material flows through complex structured networks are taken into account. This study contains the results of the analysis of the stability of solutions of differential systems of various types that simulate the transfer processes in network media. Initial boundary value problems for evolutionary equations and differential-difference systems are relevant in logistics, both for the discrete transportation of a wide range of goods and for the quasi-continuous transportation of, for example, liquid hydrocarbons. The criterion for the work of a logistics operator is the integral functional. For the mathematical description of the transport process of continuous and discrete media, a wide class of integrable functions are used, which adequately describe the transport of media with a complex internal rheological structure.

The BRICS Group unites the most rapidly developing large countries, the trade and economic interaction between which can make a significant contribution to both the region’s and world’s development. The purpose of this article is to analyze the development of trade and economic interaction and logistics infrastructure in the BRICS countries, as well as to develop an analytical concept of the BRICS Digital Logistics Platform (DLP) as a tool for the BRICS development. The research methodology includes methods for statistical data analysis, a case study of the DLP development in the BRICS countries, an analysis of the existing definitions and methods for developing DLP, and methods of systemic analysis. The research results present the trade and logistics interaction between the BRICS countries. The level of logistics development in these countries is analyzed based on the World Bank Logistics Performance Index. The article highlights the existing restrictions for the expansion of the economic interaction between countries, one of which is the uneven development of the logistics infrastructure. The article states that the BRICS DLP can be a tool for overcoming the limitation of uneven logistics infrastructure and intensifying trade interaction between the BRICS countries. The experience of creating national DLPs in each of the BRICS countries is analyzed. It is shown that the BRICS countries cannot join one of the existing national DLPs because of the risks for the national sovereignty of the participants. Therefore, an original analytical description for the international BRICS DLP is proposed. It will focus on the simplicity and transparency of the interaction between all of the participants of trade and economic interactions at various levels, as well as on the reduction of economic and logistics risks.

The goals of real business in the context of the digital transformation of international logistics networks and marketing channels have necessitated the application of a scientifically based theoretical approach to the development of a formalized description acceptable for predictive planning based on leading indicators. In the context of globalization and interstate and regional economic unions, this will lead to achieving the maximum end-to-end integration of digital platforms. Based on the analysis, the article presents the integration of digital logistics and marketing approaches with the mathematical models of the ecosystem organization of economic relations. The features of the organization of economic relations between contractors involved in the execution of virtual transactions and the material movement of resources were analyzed. The researchers considered prerequisites for the analytical description of interconnections between the participants of digital platforms in cross border e-commerce. The authors’ approach is based on the idea of both a sales funnel in marketing and a conversion funnel in digital transformation. Considering the integration of logistics and marketing, authors offer the definition of business echelons as stages of the consumer value creation. The theoretical contribution of this article consists in constructing a mathematical description of business echelons along the entire value chain. The developed analytical description of business echelons is acceptable both for embedding a digital management support system into various software products, and for conducting in-depth analysis and finding optimal solutions.