Zabolotskyy T. Modeling under alternative hypotheses in the management of a portfolio of financial assets

The dissertation is dedicated to the development of methodology of correct application of economic-mathematical tools with an aim of increasing efficiency of estimating, analysis and grounding of necessity of restructuring of portfolio on the basis of deep post optimization analysis and analysis of dynamics of changes of its main characteristics under alternative hypotheses. We justified the correctness of using of sample estimators of main characteristics of the minimum VaR (CVaR) portfolio. We develop the methodology of correct use of economic-mathematical tools in minimum VaR (CVaR) portfolio management (estimating, analysis, and grounding of necessity of restructuring) on the basis of economic-mathematical analysis of estimators of its main characteristics under alternative, relatively to classic portfolio theory, hypothesis. We present the stochastic representation of sample estimators of portfolio expected return, variance and the VaR (CVaR) which simplifies the application of imitation modeling for portfolio analysis. We proved that it is impossible to provide correct estimator of expectation of minimum VaR (CVaR) portfolio variance and variance of minimum VaR (CVaR) portfolio expected return. We develop conceptual principles of risk estimation of portfolio with the highest Sharpe ratio which is based on confidence level for VaR of the equivalent minimum VaR portfolio.