Mathematical model of fixed assets’ joint use by the machine-building enterprises

High competition in the markets of goods and services makes it urgent to improve the efficiencyof the use of production assets by the enterprises. One of the possible ways to solve the problem is joint use of the assets by different subjects. The use of this mechanism in the various branches grows rapidly in the last decade due to the opportunities for aggregation of supply and demand and automated contracting provided by the modern digital technologies. The basis for production asset management systems based on sharing is a mathematical model that allows determining the optimal modes of asset use in terms of their utilization, reducing the total cost of ownership and obtaining additional operating profit. This article considers a mathematical model of a multi-product spatially distributed production system that reflects the features of the activities of machine-building enterprises and assumes the possibility of joint use of their fixed assets. Economic and social criteria for the efficiency of fixed assets sharing are formulated in terms of maximizing the profit of enterprises, minimizing logistics and downtime costs. The optimal modes of joint use of the fixed assets concerning these criteria are investigated. It is shown that the joint use of fixed assets under the certain conditions can significantly improve the efficiency of the operating activities of enterprises.

A guaranteed deterministic approach to margining on exchange-traded derivatives market: Numerical experiment

The article discusses a modern approach to risk management of the central counterparty,primarily the issue of the sufficiency of its financial resources, including the provision of clearingmembers, the capital of the central counterparty and the mutual liability fund. The main subject is the margining system, responsible for an adequate level of collateral for clearing members, that plays critical role in risk management, being the vanguard in protecting against losses associated with default by clearing members and the most sensitive to market risk part of the central counterparty’s skin of the game. A system of margining a portfolio of options and futures in the derivatives market is described, with default management based on the methodology proposed by a number of inventors, registered in 2004. For this system, a mathematical model of margining (i.e. determining the required level of the collateral) is built, based on the ideology of a guaranteed deterministic approach to superhedging: Bellman–Isaacs equations are derived from the economic meaning of the problem. A form of these equations, convenient for calculations, is obtained. Lipschitz constants for the solutions of Bellman–Isaacs equations are estimated. A computational framework for efficient numerical solution of these equations is created. Numerical experiments are carried out on some model examples to demonstrate the efficiency of the system. These experiments also show practical implications of marginsubadditivity — a crucial property of the mathematical model.

Valuation of machinery and equipment subject to the Wiener degradation process

We propose a model describing the decrease in the market value of machines (depreciation) with age. Usually it is characterized by the percent good factor, i.e. the ratio of machine’s value to the value of similar new machinery item. Often, appraisers know about a used machinery item only by its age, but not its performance. Therefore, for the valuation of the machinery item of a known age, they have to use the mean (for machines of this age) of percent good factor. In the proposed model, the state of the machine is characterized by the intensity of the benefits it brings. In this case, the benefits from using the machine in a certain period are defined as the market value of the work performed by it minus operating costs. We describe the change in the intensity of benefits over time by the Wiener process with negative drift. This allows us to take into account the tendency for the performance of machine to deteriorate during operation. The market value of a machine is defined as the maximum mathematical expectation of the sum of discounted benefits from its use. It is shown that it corresponds to the moment the machine reaches a certain boundary state. The parameters of the Wiener process (drift and volatility) are expressed through the known characteristics of the machine's durability, namely the average value and the coefficient of variation of the service life. The dependences of the mean percent good factor of machines on the relative age (the ratio of age to the average service life) are found. It turned out that these dependencies are almost independent of the discount rate and average service life.

Optimizing the consolidated budget of the development Program for a diversified industrial complex

In a situation of economic downturn, complicated by COVID-19 pandemic, which has covered many countries in the world, including Russia, it is necessary to choose ways to ensure more or less sustainable economic growth. The condition in the Russian chemical complex is analyzed. The choice of the chemical complex as one of the priority ways of the Russian economic development has been substantiated. A conditional long-term development Program for the Russian chemical complex is worked out. This Program takes into account the shortcomings of fragmented government measures for the development of chemical and petrochemical industries. It is argued that the implementation of the Program will allow increasing the domestic supply for high-value-added hydrocarbon products, generally contributing to the reduction of the raw material share of Russian exports. The authors' earlier research to optimize structure of the development program for a large industrial complex in conditions of limited resources is developed. In particular, an approach to the choice of the optimal structure of the development program`s budget, consisting of such sources of financing as assignments from the national budget, private capital, long-term credits, as well as reinvested profit from investment projects participating in the Program is proposed. The results of economic and mathematical modeling and computer experimentation for optimizing structure of this Program`s consolidated budget, which make it possible to significantly improve its target indicators, as well as to involve socially significant low-profit investment projects of small and medium-sized businesses, are presented.

Synergetic approach to macroeconomic studies

This paper confirms the principal possibility of using synergetics in macroeconomic studies. It noted that the presence in economic systems of all science typologies requires using subjects of natural and engineering sciences for the study of economic objects as well. Ignoring this fact hinders the development of fundamental economic knowledge and, as consequence, conditions the use of metaphysical concepts in developed models. Since the above interdisciplinarity is inherent in synergetics, its applicability in macroeconomics is considered. On the example of modeling economic systems, it is demonstrated that their essence (nonlinear space-time structure) corresponds to the basic provisions of synergetics. Therefore, its tools are eligible in the tasks of macroeconomic analysis. As an example, this paper proposes the stochastic model of economic cycles explaining their phenomenon as well as providing the quantitative (parametric) description of cycles. Novelty of the model describing the cycles as random oscillations is tied to the probabilistic description of the investment function and the perception of the economic system as a material object with certain inherent properties. According to a proposed model, the income oscillations are induced by both exogenous (investment fluctuations) and endogenous (economic system elasticity) causes. The values of fluctuations of the income function around its longterm trend relate to the value of intensity of investment fluctuations as well as the gain (efficiency) of the economic system. The duration of the cycle is related to the inclusive wealth of the system and its dynamic factor, which characterizes the system’s ability to withstand investment fluctuations as well as to eliminate their consequences. Prospects of practical applications of the considered model were demonstrated on the example of cycle management.

Optimization of adaptive network economic and mathematical modeling of business planning process control

The article is devoted to the application of economic and mathematical models of business planning management based on the use of the feedback principle. As the objective function (evaluation toolkit) of the task, the value of the execution time of the entire business project, which must be minimized, is considered. To solve this problem, it is proposed to form a class of admissible strategies for optimal adaptive control of the implementation process; as well as a specific business project using network economic and mathematical modeling is worked out. Within the limits of these strategies, the method of achieving optimal self-adjusting control of business planning processes is determined, the optimal execution time and the optimal timetable for the implementation of the project are determined. The main feature of the proposed new method is the ability to take into account the real conditions for the implementation works of the concrete project, which makes it possible to timely adjust the process of management of business planning and prevent disruptions in its implementation. This method also serves as the basis for constructing numerical algorithms for the development and creating the automated systems for realization of optimal adaptive control of business planning processes. The results obtained are illustrated on a specific business project for opening a public catering enterprise and show a high degree of efficiency in using the new method.

Value-at-Risk and Expected Shortfall approaches for option premiums and the probability of default estimation based on ARMA models

The need to address the issue of risk management has given rise to a number of models for estimation the probability of default, as well as a special tool that allows to sell credit risk – a credit default swap (CDS). From the moment it appeared in 1994 until the crisis of 2008, that the CDS market was actively growing, and then sharply contracted. Currently, there is practically no CDS market in emerging economies (including Russia). This article is to improve the existing CDS valuation models by using discrete-time models that allow for more accurate assessment and forecasting of the selected asset dynamics, as well as new option pricing models that take into account the degree of risk acceptance by the option seller. This article is devoted to parametric discrete-time option pricing models that provide more accurate results than the traditional Black-Scholes continuous-time model. Improvement in the quality of assessment is achieved due to three factors: a more detailed consideration of the properties of the time series of the underlying asset (in particular, autocorrelation and heavy tails), the choice of the optimal number of parameters and the use of Value-at-Risk approach. As a result of the study, expressions were obtained for the premiums of European put and call options for a given level of risk under the assumption that the return on the underlying asset follows a stationary ARMA process with normal or Student's errors, as well as an expression for the credit spread under similar assumptions. The simplicity of the ARMA process underlying the model is a compromise between the complexity of model calibration and the quality of describing the dynamics of assets in the stock market. This approach allows to take into account both discreteness in asset pricing and take into account the current structure and the presence of interconnections for the time series of the asset under consideration (as opposed to the Black–Scholes model), which potentially allows better portfolio management in the stock market.

Economic complexity and embedding of regional economies’ structures

The research focuses on the development of localized specialization and economic diversification theories. Our task is forecasting of the emergence of new strong sectors in the region. On the basis of probabilistic and statistical modeling the model which allows estimating the probability of appearing a new strong sector in the region taking into account characteristics of economic structure is constructed. The possibility of building such a model is based on the assumption that the emergence and development of sectors is largely determined by the evolution of past economic activity. The model uses the indicators of embedding structures of the strong sectors in the regional economies is introduced by the authors. These indicators are based on the probabilistic interpretation and properties of the elements of the matrix, by which economic complexity is estimated following the traditional approach. The probability of originating a strong sector in the structure for each region is estimated. Based on sorting the sectors according to the value of these probabilities and assessments of their potential contribution to socio-economic development expert assessment of the feasibility of developing a new strong sector in the region can be made. The results show that sectors’ introduction and generation in the regional economy is largely due to the evolution of the past economic activity.