Tetiana Bolgar

The problems of mixed life insurance and insurance in the case of death are considered in the article. The actuarial present value of life insurance is found by solving a system of differential equations. The cases of both constant effective interest rates and variables, depending on the time interval, are examined. The authors used the Pontryagin maximum principle method as the most efficient one, in order to solve the problem of optimal control of the mixed life insurance value. The variable effective interest rate is considered as the control parameter. Some numerical results were given.

In the conditions of functioning of economic relations, which arise between subjects of the financial system of Ukraine, the question of creating safe conditions for their activity is increasingly being raised. Attention is paid to the investigation of the state of financial security of the country as a component of economic security, in terms of its key elements, which allows attention to the most important indicators and to develop measures to prevent existing threats.
The purpose of the paper is to forecast the level of financial security of the country based on regression analysis of impacts factors. The object of the study is the financial system as a mechanism, which is aimed at the activities of financial security subjects of the country to ensure its proper level. As a result of the regression analysis, it was found that changing in the country’s banking security by 1% will decrease the overall financial security index by 0.04 points, while the non-banking market will grow by 0.07 and the monetary component will decrease by 0.51.
Based on the calculation of the arithmetic mean of absolute deviations of independent variables, the estimated value of Ukraine’s financial security level is calculated, which is 40.09% in 2018.
Proposals for improving the “Methodological Recommendations for Calculating the Level of Economic Security of Ukraine” will help to solve the problem of mathematical substantiation of the choice of indicators for assessing financial security, minimize risks, eliminate subjectivity and improve the efficiency and the quality of the country’s financial security assessment methodology.
The article deals with the issues of the financial component of economic security as the main element of ensuring sustainable financial development of the country.