Luchakivskyy A. Economic and mathematical models of bank financial stability assessment.

The thesis is devoted to developing economic and mathematical models of evaluation, monitoring and optimization of the bank financial stability on the base of the use of multivariate, scenario and simulation concepts and estimation of economic capital. Built in the model of Z-score evaluation allows to estimate the financial stability and solvency of the first group of the largest banks in Ukraine. The conceptual approach and mathematical tools for assessment of bank financial stability in form of a scalar measure were developed in work. They are based on the application of integral calculus to the results of the bank stress tests. The binary and continuous problem of multi-objective optimization aimed to find a Pareto-efficient portfolios of assets and liabilities were built. They consist the seven objective functions and six constraints that characterize such components of the financial stability of the bank as capital adequacy, liquidity, quality passives, asset quality, the level of concentration, profitability and risk. Methods successive concessions and ? - constraints were used for realization of the different types of bank strategies through the formation of Pareto-optimal banking portfolios. The model of assessment of economic capital to cover interest rate risk is based on the use of VaR methodology and elements of GAP analysis. In work the new index of financial stability of the bank which is based on comparison of regulatory capital with economic capital, which is intended to cover unforeseen losses from bank risks was developed.