Swarm Intelligence Algorithm For Uncertain Portfolio Selection With High-order Moments

Quant investment is derived from mean-variance model by Markowitz.Since then,it is focused by the academic researcher how to use the quant method to get the optimal portfolio.Traditionally,the portfolio model is always based on the probability and fuzzy method.As we know,a premise of applying probability theory is that the obtained probability distribution is close enough to the true frequency.In order to get it,we should have enough samples.However,in real financial markets,there are situations where people have none or no sufficient historical data.In such situations,the predictions of security returns have to rely on experts' estimations.Thus,in this paper,we view the return as the uncertain variable rather than fuzzy variable or probability variable and construct the portfolio model in uncertain method.The main research work and contribution of the paper is summarized as follows:(1)We present the multi-objective uncertainty portfolio model with skewness and kurtosis,besides,according to the characteristic of the proposed model,present the modified flower pollination algorithm(MFPA).As is acknowledged that the few studies consider the effectiveness from the skewness and kurtosis in the portfolio model with uncertain method.Thus,we formulate an uncertain multi-objective mean-variance-skewness-kurtosis portfolio optimization model Then,by fuzzy programming method,we transform the proposed model into a single-objective model.Finally,we develop a MFPA algorithm to solve the corresponding optimization problem.After that,an example is given to illustrate the effectiveness of the proposed model and algorithm.(2)We develop a new portfolio optimization model in an uncertain environment using the mean-variance-skewness framework under simultaneous consideration of many realistic constraints such as transaction costs,bounds on holdings,cardinality of the portfolio,and minimum transaction lots constraints.However,the resultant portfolio selection problem in presence of the above mentioned constraints together with objective functions based on the higher order moments is NP-complete.Thus,it is difficult to solve the proposed model using traditional optimization methods.Moreover,we propose a new heuristic method termed as FA-GA,which is based on hybridization of the FA and GA.Finally,we discuss the effectiveness of the model and hybrid algorithm.