Thesis is devoted to the issues of economic and mathematical modeling of investment portfolio

In the first chapter "Classical and neoclassical approaches to the building of investment portfolio" basic categories of portfolio investment theory are described.complex analysis of main approaches to investment portfolio modeling, portfolio management tools, their application peculiarities is given. Theoretical and practical value of methods is revealed and existing imperfections are mentioned. Worked out and suggested economic and mathematical modeling of investment portfolio classification.

Actual methods of creating optimal investment portfolio by one or another criterion are divided into two groups: classical and neoclassical.

Classical methods are based on hypothesis of invariability of security yield distribution average and fluctuations relating to it are characterized by constant - standard deviation. Neoclassical methods mean other ways of expected yield and risk estimation, also, there are other differences between approaches.

Most of issues on optimization of investment portfolio are lacking attention to discussing of methods efficiency. Proved statements and conclusions obtained on experimental data are very rare. Necessity of proving of newly created portfolio model efficiency and advantages is asserted.

The second chapter “Application of noncausal methods of economic forecasting at investment portfolio formation and management” is devoted to investigation of efficiency of application of some noncausal forecasting methods to security prices dynamics with aim of obtaining the best input estimation of future yield for investment portfolio optimization model. Special attention is paid to analysis of historical data quality and estimation of forecasting accuracy. Substantial interpretation of obtained results is included.

Trend models, exponential smoothing model, Halt-Winters model, autoregressive moving average model (Box-Jenkins model) are built. Defined that the best methods of forecasting is ARMA-ARIMA forecasting method, a bit worse Halt-Winters method and other methods are far worse. ARMA-ARIMA forecasts of share yield are better in most cases than according selected average values.

In the third chapter “New models of investment portfolio formation and management. Practical calculations and results" an efficiency of application of traditional and some of alternative estimation of yield and risk in investment portfolio modeling is investigated. New risk criteria and methods of involving historical data are suggested. Developed by author economic and mathematical models of investment portfolio choice: investment portfolio model with Poisson’s smoothing and taking preferences into account; investment portfolio structure optimization models with indication of possible loss of yield; models of optimization of securities packages size. Recommendations on their application are given. Practical results of modeling are commented and analyzed. Conclusions on successfulness and practical usefulness of application of worked out methods and models are made.

Methodological basement of investment portfolio model with Poisson’s smoothing and involving preferences is Markovitz approach. Portfolio that provide obtaining set yield with minimal risk is defined. As risk measure for financial assets average square of yield increases for past time intervals is taken instead of variation. For description of non equal periods of market functioning and considering corresponding influence on previous data Poisson’s smoothing is used. Methods of considering individual preferences of investor relative to financial assets are suggested. Model represents assets liquidity and financial state of their issuers. Use of the model for choice of investment portfolio with real data of Ukrainian capital market proved its practical value.

Investigation of application of traditional and alternative methods of yield and risk estimation in model of investment portfolio resulted that ARIMA forecast is better method of yield estimation than selected average and average square of increases is better risk estimation than variation. Model using that results is suggested. Noted that alternative risk criteria of investment portfolio can be created by using Box-Jenkins forecasts. New risk estimations and models applying them are suggested. Relative simplicity of using and solving linear models of investment portfolio is noted. Ways of the most adequate considering of real conditions of portfolio investment in models of securities packages size optimization are given. These models are proposed for consideration as object of further development till state of ready to practical use.

Key words: investment portfolio, economic and mathematical modeling, forecasting, financial assets, yield, risk.

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