The Ukrainian market of insurance services is at the stage of formation and development in the absence of a clearly defined model for further functioning. The purpose of the paper is to analyze the trends in the functioning of the Ukrainian insurance services market in the period of 2010–2021.The results of the study reveal the general trends in the functioning of the Ukrainian insurance services market in terms of transformational features of the market composition (a significant reduction in the number of insurers – by 2.5 times), concluded insurance contracts (a significant increase by 3.5 times), market concentration (moderately concentrated), the level of insurance penetration (the average value was 1.64%).Considerable attention is paid to the interpretation of the main indicators of market activity and their dynamics, in particular, in terms of insurance premiums and payments (the level of insurance payments was 32.2%), assets of insurers (increase by 1.5 times), formed insurance reserves (a noticeable increase by 3 times), digital transformation (in terms of internetization, individualization, digitalization).The study made it possible to form promising vectors for the development of the Ukrainian insurance services market based on the model of social responsibility of participants in the insurance process with clear digitalization outlines and the formation of insurance relations based on innovative approaches. AcknowledgmentThis study was supported by the Ministry of education, science, research and sport of the Slovak Republic [grant VEGA 1/0689/20 Digital economy and changes in the education system to reflect labour market demands].

Under the conditions of the development of market relations, the insurance protection of agricultural producers plays an essential role in the economic stabilization of their development. Insurance can be one of the most effective tools for managing production, market and legal risks, but agricultural insurance is not well developed in the country. The purpose of the article is to study the current state and prospects for further development of the Ukrainian agrarian insurance system, based on developing the strategy of development of the latter with maximum consideration of needs and interests of all its participants.General scientific methods of scientific knowledge and research of economic phenomena are used for the achievement of the goal set in the article, such as the abstract-logical method, comparison method, monographic method, tabular method, graphical and scientific generalization.The article investigates features of the present state and general tendencies of functioning of the Ukrainian agrarian insurance system and outlines general features and prospects of further development of the latter, which are based on development of the strategy of system development with maximum consideration of needs and interests of all its participants. A set of principles is defined on which the strategy of development of the Ukrainian agricultural insurance system should be based and their further functioning in the format of the model of private-public partnership is proposed within the framework of the developed strategy. This represents a balance between public-private partnerships. The results of the study can be used for further scientific developments in this direction. The implementation of the measures proposed in the framework of the strategy for the development of the Ukrainian agrarian insurance system through the effective use of state resources and maximum use of the agrarian market and the insurance market should ensure stability of both agricultural production in general and income of the rural population in particular. This is a prerequisite for stable economic growth of the country and an increase in the welfare of its citizens.

In the article a parallel between the classical and parametric scheme of agricultural risk insurance is conducted. The application aspects of parametric (index) schemes of insurance with emphasis on the use of weather index insurance products are examined, their advantages and disadvantages are considered. This research examined the applicability along with simple weather index insurance products combined, that can consider and put together a few parameters simultaneously and thus neutralize the impact of the whole weather risks at regional level. The authors demonstrated the feasibility of using the proposed combination of weather index (C i)-a special indicator which characterize the impact of weather risk combitation intensity, measured by certain parameters (heat, cold → temperature; air humidification → relative humidity; drought → precipitation) on the grain maize yield in definite growth stages (flowering and grain filling). On the basis of research, the detail mechanism proposed by the authors of the combined weather index (Ci) in general, and on the example of concreate calculations, is performed in particular.

This article justifies the use of a new methodical approach to index insurance of agricultural producers against weather risks, in particular, the use of the thermal-hydraulic combined index (Іth) as the weather index of the effect of several triggers (temperature and precipitation) on yields, taking into account the uniformity of weather and climatic conditions over time. General scientific methods of scientific knowledge and research of economic phenomena are used for the scientific solution. The theoretical and methodological bases of the research are the works of scientists and practitioners involved in researching the market of agricultural insurance services in general and the issues of developing an effective system of agrarian insurance, in particular. The main method of research is the method of mathematical statistics, namely, a multivariate analysis of variance. This article presents research on the application of index insurance schemes while using weather index products. The advantages and disadvantages of these products are considered and the mechanism of the index insurance is described in general. The article considers the possibility of applying a rainfall index with a temperature threshold, and the thermal-hydraulic index (Іth) that takes into account and simultaneously combines several parameters is calculated. Considering the research findings, the authors suggest the adoption of the compound thermalhydraulic index (Іth) and present a detailed description of the functioning of this mechanism. Approbation of the methodological tools was carried out on the example of the Uman District of the Cherkasy Region of central Ukraine.

Based on the current situation, it is necessary to review the mechanisms for providing state support which will be of a combined nature and also change priorities. In particular, more attention should be paid to individual, family and farming enterprises, for which the direct financial support will be more convenient. Separately, it is worth revising the taxation of the livestock sector of the economy, as well as encouraging the integration of small farms into cooperatives.