The article formulated and implemented the conceptual statement of the problem of constructing a mathematical model consisting in obtaining the function of interpolation, as well as a mathematical statement, which found an expression in the calculation of local extremes of the cubic polynomial weight of social expenditures of the state budget. As a fundamental assumption of the macro-level model of budget support for social risk management, the approach is set out in the ESSPROS methodology - the social protection and social security system should be the main compensatory mechanism for social risks. The construction of the interpolation function of the specific weight of the state budget expenditures on social protection and social security in total expenditures is carried out in the computing algorithms environment Wolfram | Alpha. The constructed mathematical model of budget support for social risk management provided an opportunity to obtain a mathematical algorithm, which formalized the uncertainty situation related to the probabilistic nature of the risk manifestation and made appropriate projected estimates.

social risks, interpolation function, probability, social protection, social security, management function

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1. Kluppelberg, C. (2016). Risk – a Multidisciplinary Introduction. [Karl F. Bannör and Matthias Scherer Model Risk and Uncertainty – Illustrated ith Examples from Mathematical Finance]: Springer International PU [in English].

2. Boiarchuk, T. (2006). Formuvannia systemy otsinky i rehuliuvannia sotsialnoho zakhystu naselennia [Formation of a system of assessment and regulation of social protection of the population]. Lviv. [in Ukrainian].

3. Proskura, V., Bilak R. (2017). Metodolohichni pidkhody do upravlinnia ryzykamy [Methodological approaches to risk management]. Ekonomika i suspilstvo. 9. 599–607 [in Ukrainian].

4. Oliinyk, Y., Bobrovytskyi A. (2017). Modeliuvannia rozvytku ekonomiky Ukrainy z urakhuvanniam intehratsii v rehionalni ta svitovi systemy vzaiemovidnosyn [Modeling of the development of Ukraine's economy, taking into account integration into regional and world systems of interrelations]. Chasopys sotsialno-ekonomichnoi heohrafii. 22. 32–38 [in Ukrainian].

5. Savastieieva, O. (2017). Ryzyky efektyvnosti biudzhetnoho protsesu na rivni terytorialnykh hromad [Risks to the effectiveness of the budget process at the level of territorial communities]. Naukovyi visnyk Mizhnarodnoho humanitarnoho universytetu. 2. 92–95 [in Ukrainian].

6. Metodolohichni polozhennia shchodo skladannia dopomizhnykh (satelitnykh) rakhunkiv sotsialnoho zakhystu v Ukraini [Methodological provisions for the compilation of auxiliary (satellite) accounts of social protection in Ukraine]. (2010). ukrstat.org. Retrieved from http://ukrstat.org/uk/metod_polog/metod_doc/2010/56/metod.htm [in Ukrainian].

7. Antoniuk, P. (2008) Sotsialni ryzyky yak determinanta sotsialnoho zakhystu naselennia [Social risks as determinants of social protection of the population]. Visnyk Khmelnytskoho natsionalnoho universytetu. 2( 2). 96–99 [in Ukrainian].

8. Wolfram Alpha. Calculus&Analysis. (2018). www.wolframalpha.com. Retrieved from http://www.wolframalpha.com/examples/mathematics/calculus-and-analysis/ [in English].

9. Trease, H., Fritts, M. and Crowley, W. (2014). Advances in the Free-Lagrange Method. Berlin: Springer Berlin [in English].

10. De Clerck, J. (2014). Topics in modal analysis I, vol. 7. Cham (Alemania): Springer [in English].

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