Kroptya A. Multivariate risk models in enterprise decision support systems

The dissertation is dedicated to development of a complex system model and application methodology with probability multivariate risk models, for complex financial and economic systems, in informational risk management decision support systems. Based on analysis of risk estimation and management problem, argued urgency of modeling risk with nonlinear asymmetric interaction problem. Developed а new method for risk characteristics distribution construction by combining generalized Pareto distribution and normal distribution in joint model for extremely large and common risk values. Proposed quantitative risk evaluation through risk profile build from quantitative risk measures and deviation measures, for evaluation loss values risk and loss uncertainty risk at the same time. Proposed multivariate risk modeling of dependent risks based on marginal combined distributions and copulas. Active risk management portfolio optimal structure problem was solved by flexible multivariate joint distribution modeling. In thesis proved usefulness of developed methods for number of risk factors determination in economic system by analysis eigenvalues of correlation and concordance matrices. Proposed models and methods are implemented in decision support system for Ukrainian Railways.