Fuzzy Decision Method Of Optimal Portfolio Problem

Recently, the practical factors of portfolio problem often has some ambiguity,on the other hand, the portfolio problem with constrains such as transaction costs andwithout short-selling prohibition is an NP-complete problem, therefore, by using thefuzzy theory and decision method and the modern optimization algorithm to solve theportfolio problem has become a research emphasis and hot spot.In this paper, fuzzy decision making and hybrid intelligent algorithms are discussedto solve the constrained stock-bond portfolio problem. The main work is summarizedas follows:1. For portfolio selection with V-type half absolute deviation risk transaction costfunction, new nonlinear membership functions about investment income targetlevel and risk target level psychological satisfaction are given. Then make anonlinear satisfaction investors portfolio selection model into a standard linearprogramming model, and proof the equivalence of the two model. Finally,practical example illustrates feasibility of the obtained model.2. For trading unit, transaction costs and other constraints in securities trading market,the function of stock-bonds semi absolute deviation risk is proposed.Consideringconstraints such as not buying empty, no short sales, transaction fees, tradingunits and other practical,the mathematical model of stock-bond portfolio selectionis established. Based cuckoo search algorithm and firefly algorithm,a hybridintelligent algorithm is presented which combines their advantages and enhancesthe ability of search optimal solution. Finally, an actual example illustrates theeffectiveness of the obtained algorithm.