This article is devoted to the further development of feedback loop models. They are used in the management of a single-industry firm. The development of the studying consists in the mathematical modeling of transients and assessing their impact on economic indicators. To solve this problem, the following was done in the article. A structural model of the functioning of a single-industry firm (SIF) is presented. It is built in accordance with the theory of automatic control (TAC) and includes elements: a management unit, a production unit, a sales unit, information nodes, as well as a feedback loop (FL). Equations and relationships describing the logic of the functioning of the company as a production system are presented. They allowed us to derive dynamic relationships and differential equations that reflect feedback loops on revenue and production costs. The system of expressions in operator form is presented, which describes the contour of the FL SIF. It has the form of a system of differential equations. It forms the basis of the mathematical model of SIF in the control system. This model made it possible to obtain a graphical interpretation of transients with closed and open FL based on the use of the Mathcad editor. Transients are fluctuations in sales volumes and production costs in the presence of disturbing influences. This is the scientific result and determines the novelty of the article.
Delta-neutral trading strategies for trading volatility allow you to make a profit regardless of the direction of change in the price of the underlying asset. Despite their popularity and high efficiency, they are usually made manually, which makes them less systematic and vulnerable to the negative influence of the human factor (emotions, late actions, erroneous submission of applications, etc.). The article proposes a unified delta- neutral strategy, taking into account several parameters for long-term volatility trading through transactions with underlying assets (futures or stocks) and options on these underlying assets, which creates prerequisites for its automation. The use of the strategy helps to increase the liquidity of investment assets traded on the exchange, increases the receipt of taxes, exchange fees and commissions, which brings great socio-economic benefits. Automation of the strategy significantly simplifies calculations, increases the speed of decision-making and can significantly increase the number of transactions made in the financial markets. In addition, the automatic calculation of the optimal values of the method parameters can make a significant contribution to the theoretical research of the modifications of the volatility trading methods.
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