Advanced computational methods in portfolio optimisation

Portfolio optimisation is the process of making optimal investment decisions, where a set of assets are selected and invested with certain amount of the capital in the portfolio. Since the milestone work, Markowitz’s Mean-Variance (MV) model, it has boosted the research for new portfolio optimisation models and applications for last 60 years. Despite its theoretical values, the MV model has been widely criticised for underlying simplistic assumptions which ignore real world conditions and fail to take the market uncertainty of the mean and variance into account. To correct these, a large number of models have been developed. When additional features are extended to the traditional MV model, normally it makers the problem more difficult to solve, such as the introduction of some practical constraints makes the problem NP-hard. The aim of this thesis is to study various techniques for solving portfolio optimisation problems with different features. In the first stage of this thesis, it is mainly focused on portfolio optimisation problems based on MV model with gradually more complex real world constraints. Firstly, a hybrid approach is investigated which utilises exact and metaheuristic methods to optimise asset selection and capital allocation in portfolio optimisation with cardinality and quantity constraints considered respectively. The proposed method is composed of a mathematical programming application and customised population based incremental learning procedure. Then the metaheuristic technique is studied where a variable neighbourhood search approach with compound neighbourhoods is developed to solve the portfolio optimisation problem with four additional practical constraints (cardinality, quantity, pre-assignment and round-lot). Due to the fast development of the state-of-the-art commercial solver, it motivates us to study the performance of exact solver for various practical constrained MV model based problems. In the second stage of this thesis, my interest of the portfolio optimisation problems focuses on a more complicated domain where stochastic programming is considered to capture the market uncertainties in terms of future asset prices. In addition, an alternative risk measure, one of the most recent downside risk measures, CVaR is adopted. Consequently a two-stage recourse model with CVaR as risk measure and a comprehensive set of practical constraints is investigated by a hybrid scheme which utilises exact and metaheuristic methods. In this study, two hybrid approach are implemented and studie