Probabilistic Numerical Methods and Target-Based Investment Strategies for Dynamic Portfolio Optimization

This thesis develops a numerical approximation method for how to invest in, and how to dynamically adjust the capital allocation to different classes of financial assets, in the presence of realistic trading features such as transaction costs and liquidity effects. A family of novel investment strategies is developed. These strategies aim to track a specified investment target which can be labelled in terms of absolute return, relative return, realized volatility, maximum drawdown and any other risks and uncertain variables that may draw concerns to investors.