Riabushenko A. Applications of portfolio investment modelling

The thesis is dedicated to the research of novel mathematical models and method in financial engineering.The proposed models and method are used to form the basis for the portfolio investment system developed on system analysis principles. The statistical analysis in Ukrainian securities market was carried out. It was shown that this market requires improved financial engineering models for taking into account identified statistical properties. The following models and method in the financial engineering are introduced: portfolio optimization model, derivatives pricing model - "stochastic mean multifractal volatility model" and risk estimation method - "nonparametric Monte Carlo". Based on principles of system analysis, the unified model of portfolio investment system was proposed. The system provides desired features: efficiency, scalability, extensibility, reliability, transparency and low total cost of ownership.