Evolutionary Algorithms For Multiobjective Portfolio Problems

Portfolio problems concern about how to appropriately invest the capital in a series assets to achieve the highest return under a given risk level.Modern portfolio theory is first introduced by Markowitz in 1952,he utilizes statistical methods to ingeniously quantify the return and risk of assets to build mathematical models for the problems.This profound and systematic theoretical study earns him the Nobel Prize in Economics.With the gradual development of the global financial market,the significance of portfolio problems has become increasingly significant.However,in real application scenarios,investors often introduce many complex factors when constructing problem models based on the portfolio theory.These portfolio problems will involve tricky issues,namely,multiobjective,constrained,mixed-integer problems.This doctoral dissertation discusses how to develop and apply evolutionary algorithms for several classic portfolio models.The main work of this paper is listed as following:1.A compressed coding scheme(CCS)is proposed for general multiobjective models and it is incorporated into existing MOEA frameworks.In order to suit the one-to-one dependence between variables,the asset selection(integer variable)and capital allocation(real variable),a tailored coding scheme is devised.There are some superiorities for this scheme,such as converting the original mixed-integer problems into simpler continue problems,the ability of reusing existing operators,utilizing the dependence between variables.In the experimental analysis,we first carry out a simulation experiment by incorporating the compressed and hybrid coding into the MOEAs respectively.It verifies the superiority of the compressed coding scheme.Then,the CCS-MOEA is compared with the tailored MOEAs on portfolio problems,and the former shows better performance and robustness.2.An MOEA based on Pareto front evolution(F-MOEA/D)is proposed for the Mean-Variance(M-V)model.The M-V model is a classical quadratic programming problem,but neither an evolutionary algorithm nor an exact algorithm can effectively deal with the M-V model under complex constraints.In this paper,the evolutionary algorithm and exact algorithm are organically combined,and the evolutionary algorithm is employed to search for the asset selection(integer variable),and then the exact algorithm is used to find the capital allocation(real variable).In this manner,the proposed algorithm has a unique evolutionary structure,and each solution in the population is a local Pareto front rather than a single data point.This algorithm makes up for the shortcomings that an MOEA can only find approximate optimal solutions and an exact mathematical programming method can only solve small-scale problems.Hence,it achieves a balance between efficiency and effectiveness.The experimental results clarify that F-MOEA/D has better performance for convergence when compared with the MOEAs.It also shows that F-MOEA/D finds similar/better solutions on small/largescale problems when compared to the exact algorithms.3.An MOEA based on a local and a multi-stage search strategy(MSL-MOEA)is proposed for the Mean-Value-at-risk(M-Va R)model.The M-Va R model is a non-differentiable,multi-extremal,and non-convex problem.Exact algorithms can no longer be employed for solving these problems.Therefore,this paper proposes a local search method for tackling non-convex problems.With the help of the local search method,the algorithm can improve the accuracy of the solutions by constructing local Pareto fronts.Moreover,the algorithm also introduces a multi-stage search strategy.For uncertain solutions,this strategy will call evolutionary algorithms to evaluate them roughly.For a good asset selection,this strategy utilizes a local search method to construct its local Pareto front.The multi-stage search strategy not only improves the accuracy of the solutions,but also reduces unnecessary computing costs indeed.The results of simulation experiments verify the performance of MSE-MOEA when it is likely to find very competitive solutions in a relatively short time.4.An MOEA based on an exact method and a multi-stage search strategy(MSE-MOEA)is proposed for the Mean-Conditional value-at-risk(M-CVa R)model.The M-CVa R model is a linear programming problem.Linear programming problems are very easy to solve for exact algorithms.However,when the M-CVa R model involves complex practical constraints,the efficiency of the exact algorithm will enormously decline.On large-scale M-CVa R problems,it is not suitable to invoke the exact algorithms as usual.Therefore,the multi-stage search strategy will continue to be employed.An alteration for the remodeling is made due to the characteristics of M-CVa R model.Meanwhile,a linear programming method instead of the local search approach is applied for constructing the local Pareto fronts.The experimental analysis shows that the exact algorithm can effectively improve the accuracy of the results when we compare MSE-MOEA to MSL-MOEA.Moreover,according to the experimental results,MSE-MOEA outperforms the alternative algorithms.