| In order to meet the increasing demand of people for finance and investment,a variety of investment products have been provided by financial enterprises and institutions.Actually,the investment can be described as the behavior of that the economic subjects expect to obtain higher returns in areas of risk on capital.Under a given level of risk,how to make the investors get benefits as much as possible,or to reduce the risk of investment as low as possible under a given level of income.The most practical way is investment portfolio which diversify investment fund scientifically on multiple products.The investment portfolio can take advantage of the high return on the successful investment,to make up for the capital loss of the unsuccessful investment.So that the risk of investment can be effectively reduced while ensuring future returns.Essentially,the investment portfolio selection is usually a constrained optimization problem.Compared with the traditional mathematical method,stochastic ranking evolutionary strategy as a kind of intelligent optimization algorithm,can be more flexible to deal with a series of challenges in investment portfolio problem,such as the infinite combination mode and complicated constraints.Many real investment restrictions are considered in the classical Markowitz mean-variance model in this paper.And then some realistic investment portfolio models with constraints are designed,including single-objective or multi-objective respectively.Moreover,stochastic ranking evolutionary strategy is applied to solve the single-objective model,as well as the multi-objective model.Firstly,the reality restrictions such as short-selling and transaction costs are not taken into account in the classical model.However,in order to avoid the risk of settlement,the trade of short-selling are not expected and a certain transaction fee should be paid for each real investment trade in the China's Financial Market.Combined with these two restrictions in our investment portfolio,we design a single-objective investment portfolio model with constraints on short-selling and transaction costs restrictions.Furthermore,the algorithm of stochastic ranking evolutionary strategy is applied to this model,and the application experiments are conducted on 9 kinds of stock data sets,such as Wuhan Iron & Steel and so on.The experimental results show that the stochastic ranking evolutionary strategy has a better investment portfolio solution than the penalty function method because of its good constraint handling ability and penalty-free parameter characteristics.Secondly,the investment share of the single-objective model is allowed to be divided indefinitely,but it can only choose one as the objective from the benefit and risk,also the model only has one optimal investment portfolio solution.Combining the limitation of the minimum trading unit in the actual financial products,we design a multi-objective investment portfolio model with minimum trading unit constraints which considers income and the risk simultaneously.In view of the good constraint handling effect of stochastic ranking mechanism in the single-objective optimization,we further utilize the scalar objective properties of each sub-problem and the stochastic ranking mechanism.The former is computed from the multi-objective evolutionary algorithm based on decomposition(MOEA/D).And the last one is integrated into the MOEA/D framework to deal with the constraints.The whole algorithm is used to solve the multi-objective investment portfolio model on 9 stock data sets with minimum trading units.The experimental results show that the MOEA/D algorithm combined with stochastic ranking can effectively obtain a set of several better feasible investment portfolio solutions under different income level conditions,which is beneficial to the investors to select the most suitable investment portfolio from the effective boundary of the above-mentioned optimal solution set according to their preference for risk-return. |
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