• data-driven method
• Mean Variance
• Kelly
• Markowitz
• nonparametric
• Portfolio optimization

Portfolio optimization is a very classical and challenging problem that is interested in many areas of science such as computer science, mathematics and operations research. In this dissertation, this problem will be approached under minimal assumptions to make the models able to be applied to the real world where the market is not static. Two major portfolio theories of Markowitz and Kelly besides other theoretical analysis are detailed in a logic way to lead to the vital ideas in constructing models for portfolio selection. The Gyorfi nonparametric method and Machine learning are applied to construct data-driven optimal portfolio in the model of dynamic investment. Moreover, the new proposed models in this dissertation take into account the risk averse behaviour, which is commonly ignored in portfolio optimization method focusing in the growth of wealth, of not only investor but also experts, who make advice in the model of experts learning. The algorithms for portfolio selection models are built and performed to compare, measure and analysis their performance with each other and with benchmark strategies using the real data of stock market NYSE. The results analysis demonstrates the positive effects of behaviour of investor and experts on the improvement of portfolio strategy in term of measurement such as growth of wealth, Sharpe ratio and Sortino ratio in volatile stock market.