The article presents innovative approaches to improving the risk management process in the context of developing a strategy for foreign economic activity of enterprise. To identify risks and choose the optimal strategy for foreign economic activity of enterprises (FEA), economic and mathematical modelling was used using the risk matrix and the criteria of Bayes, Laplace, Wald, Savage, Hurwitz, Hodge-Lehman. To approbate the results of the study, enterprises of the pharmaceutical industry were selected. According to the theory of games, in order to improve the risk management process, elements of the payment matrix have been applied, which characterize the profit of pharmaceutical enterprises in foreign economic activity. The use of the Hurwitz criterion, which is a criterion of pessimism-optimism, made it possible to choose the optimal strategy for the selected enterprises. The developed matrix of risks of foreign economic activity (strategic, operational, financial and external) for the selection of the optimal strategy of foreign economic activity through the use of economic and mathematical modelling should be used to determine the risks of the greatest impact at different stages of foreign economic activity using the theory of games. The presented matrix of risks of foreign economic activity is built for domestic enterprises of the pharmaceutical industry and is aimed at improving the process of risk management of foreign economic activity, which will enable enterprises of the pharmaceutical industry to predict risks at the early stages of activity and take into account in the general concept of the strategy of foreign economic activity of enterprises. The pharmaceutical industry of Ukraine was chosen for research because it is the most popular in modern conditions, and, according to the results of the analytical review, very high-risk. That is why the use of economic and mathematical modelling for risk calculation allows to optimize the economic behaviour of domestic pharmaceutical enterprises, while providing a reliable basis for making sound strategic decisions in the process of risk management in the context of developing a strategy for foreign economic activity. The risk management process, consisting of 7 stages and 18 steps, has been improved, and innovative tools have been proposed that facilitate the implementation of risk management in the enterprise in the process of developing a foreign trade strategy. The use of economic and mathematical modelling in risk forecasting and the formation of a foreign economic activity strategy will help enterprise managers to significantly increase management efficiency, reduce risks at the stage of planning foreign economic activity. The article improves the risk management process, which consists of 7 stages and 18 steps, and offers innovative tools that facilitate the implementation of risk management in the enterprise in the process of developing a foreign trade strategy. The use of economic and mathematical modelling in risk forecasting and the formation of a foreign economic activity strategy will help enterprise managers to significantly increase management efficiency, reduce risks at the stage of planning foreign economic activity.
