Purpose. The purpose of the paper is to study the state, perspective directions of Ukrainian exports of agricultural products and the introduction of effective forecasting using the method of mathematical modeling of a continuous system of aperiodic components. Methodology / approach. In the process of research, the fundamental provisions of modern economic science were used in relation to the groups of factors influencing the resulting indicators of export, foreign trade trends, methods of statistical analysis to assess the weight of factors influencing the resulting function, as well as modern mathematical methods for forecasting of agrarian exports were implemented. Results. The application of the developed mathematical model and the algorithm based on it, allowed to study the situation with the export of Ukrainian agricultural products to the EU, to identify trends specific to individual countries and the EU market as a whole, to assess the opportunities and prospects of niche markets, expansion nomenclature of export goods. Prognoses were given both on the export prospects of individual goods, product groups, and on the volume of deliveries to the EU. The use of factor analysis for forecasting of export deliveries allowed us to assess the impact of each of the factors and limit their amount. Originality / scientific novelty. For the first time, the method of mathematical modeling of a continuous system based on changes in its aperiodic components was used for efficient and relevant forecasting of agrarian export volumes. Even the stages of application of this method, in particular, the analysis and prognoses for individual items of the nomenclature of export goods, for individual countries – importers make it possible to represent the situation with agrarian exports more accurately and forecast future supplies. Practical value / importance. The proposed mathematical approach for market analysis and forecasting of markets can be used by both market regulators and producers and exporters of agricultural products. These polynomial equations for analysis and prognostication for individual product groups can be directly used in practice.

Based on the analysis of the problems of agriculture of Ukraine the author highlighted categories of problems of agriculture in Ukraine and with the help of the Thomas L. Saaty analytic hierarchy process and identified their rating. The next stage of the rating definitions and problems is the pairwise comparisons of each problem category. The first place in the category value is "economic", the second-"infrastructure", the third-"social", and the fourth-"production", in the last fifth place-"environmental" problems. According to the analysis in each category is provided a list of the main problems of agriculture in Ukraine: small-scale production, insufficient condition of fruit and vegetable warehouses, weakness of non-productive cooperatives, rising unemployment, opacity of land relations, inconsistency with international standards of quality and safety, low investment adaptation of Ukrainian legal acts to EU requirements, unsatisfactory condition of engineering and transport infrastructure of rural settlements, lack of technical support for producers of agricultural machinery and low-sales service, non-compliance with agricultural storage technologies, running state of social infrastructure and other.

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