Fuzzy Portfolio Theory With Transaction Costs

Since Markowitz put introduce mathematics ideas to the portfolio,the portfo-lio has become a hot research direction，because of the complexity and instabilityof the investment environment,making it difcult for researchers to build a com-plete portfolio model.So,diferent research from diferent angles to create a timemodel,use diferent mathematics thought to solve the portfolio problem.In this paper, we are base on the interval planning method to study thefuzzy portfolio selection model under diferent transaction costs.In the valuationof the interval number, the introduction of a normal membership function, andthe correction of future returns amount,consider a realistic factors-price limits;the introduction of a new defnition of liquidity, to correct the defects of the pre-vious turnover studies brought. Through the above methods, the establishmentof a new fuzzy model of portfolio investment adjustment strategy in the diferenttransaction cost.The frst chapter introduces the research background and research status offuzzy portfolio selection problem and artifcial fsh swarm algorithm.The second chapter states the general portfolio, introduces something aboutfuture earnings, preference factor,and mobility what is establish the model andsolve the model by the use of the knowledge points.The third chapter establishes the model of portfolio investment with a fxedtransaction costs,the model uses the absolute deviation as a risk function,throughcontinuous deformation, which was transformed into a linear model.The fourth chapter established a transaction costs as the portfolio model ofconvex function,which involved a range of numbers, so when the model used inthe calculation of the conversion interval number.The ffth chapter from the Shanghai stock exchange market selection5difer-ent stocks,the artifcial fsh swarm algorithm for data simulation, the combinationof investors in diferent risk preference.