Hybridising metaheuristics and exact methods for portfolio optimisation problem

This thesis focuses on the portfolio optimisation problems, which concern with allocating the limited capital to invest in a number of potential assets (investments) in order to achieve the investors risk appetites and the return objectives. In the 1950s, Harry Markowitz proposed a mean-variance portfolio optimisation model, which is widely regarded as the foundation of the modern portfolio theory. However, the basic Markowitz mean-variance model has limited practical utilities since it omits many constraints existed in real world trading. The problem quickly becomes more complex with the additional real-world trading constraints involved. One main problem of the mean-variance portfolio optimisation framework is that it relies on the perfect information. In practice, the problems faced in portfolio optimisation are more complex since many sources of market uncertainty are involved. Moreover, different risk measures need to be adopted in order to have a better reflection of the asymmetry nature of asset returns. The thesis firstly studies the single-period mean-variance portfolio optimisation model with two practical trading constraints. Hereafter, a two-stage scenario-based stochastic portfolio optimisation model is developed. The two-stage stochastic programming model minimises the excess shortfall of portfolios which are captured by the CVaR risk measure. The two-stage stochastic programming model can capture the market uncertainty in terms of future asset prices and it enables the investors rebalancing the assets in a dynamic setting. A copula-based method is applied to generate scenarios to represent uncertainty in future asset prices in accordance with their historical information. Stability tests are also performed and the results confirm that the scenario generation method is appropriate for the model. Three hybrid algorithms which hybridise metaheuristics and exact methods in an integrated manner are presented to solve the two models. The principle of designing hybrid methods in this thesis can be described as: metaheuristic algorithms are adopted to search for the assets combination heuristically and exact methods are applied to calculate the corresponding assets weights optimally. For the cardinality constrained mean-variance model, a combinatorial algorithm which hybridises a PSO and the mathematical programming method is proposed to address the problem. For the two-stage stochastic programming model, a hybrid algorithm which integrates a GA and a LP solver is presented to address the problem and a hybrid combinatorial approach which integrates a PBIL-based metaheuristic and a LP solver is developed to address the problem with a large number of scenarios. One main advantage of the hybridisation approach is that it can guarantee the optimal weight allocation of the identified asset combinations. Some useful strategies for different metaheuristics are investigated in order to keep a balance between algorithms' exploration and exploitation. Some useful mechanisms are also adopted in order to enhance the search efficiency and achieve a global better performance. The results have shown that such hybridisation strategy can achieve synergetic effects through the integration of multiple components