Research On Portfolio Selection Model And Decision Of Financial Assets Under Uncertain Environment

Portfolio selection refers to that investors allocate funds to different assets according to a certain proportion in order to achieve the purpose of dispersing risks and improving returns.Markowitz(1952)gave the mean-variance portfolio model,which marked the birth of portfolio theory.Since then,it has attracted a large number of experts and scholars to further improve the portfolio theory.However,these studies were conducted in the random environment.In fact,the financial market is very complex,and the historical data of the rate of financial assets returns can not reflect the future returns of financial assets very well,and there are still many cases of lack of historical data,which requires experts to estimate the returns rate of financial assets based on their knowledge and judgment.This paper discusses the portfolio selection of financial assets under uncertain environment.The paper applies uncertainty theory to portfolio management of securities and futures,and establishes respectively uncertain portfolio selection model with realistic constraints,mental account and background risk and futures uncertain selection portfolio model with leverage.The specific research contents and innovations are as follows:(1)The uncertain portfolio selection model with realistic constraints is constructed.In the past,scholars seldom considered realistic constraints,or only considered transaction costs and whole-hand transaction constraints when they studied uncertain portfolio selection.However,in the actual investment process,investors often need to consider the liquidity risk of securities,security diversification and sector diversification constraints.In view of this,the paper introduces uncertain variables to describe the security return rates.On the basis of considering transaction costs and whole-hand transactions,the paper further considers the liquidity risk of securities,security diversification and sector diversification constraints,and constructs the uncertain portfolio selection model with realistic constraints.In order to solve the model easily,the equivalent form of the model is deduced in the paper.The uncertain portfolio selection model constructed in the paper is very complex and difficult to solve by traditional methods.Aiming at the difficulty of solving the model,the paper uses genetic algorithm to solve the model.Finally,numerical examples are given to illustrate and analyze the scientificity and rationality of the model.(2)The paper establishes uncertain portfolio selection model with realistic constraints,mental account and background risk.Investors always divide funds into different sub-accounts to manage,and in the process of investment,besides facing the risk of price change of financial assets,they must also face their own background risks.Therefore,we need to take account of mental account and background risk in the process of building the model.We assume that both the returns of securities and the return of background assets are estimated by experts.Based on the consideration of realistic constraints,the paper constructs the uncertain portfolio selection model with realistic constraints,mental account and background risks.In order to solve the model easily,the paper derives the equivalent form of the model.Finally,numerical examples are given to illustrate and analyze the scientificity and rationality of the model.(3)A futures uncertain portfolio selection model is constructed to solve the problem of capital proportion and optimal leverage once for each futures.Previous scholars' research on futures portfolio management has constructed different types of futures portfolio selection models without the leverage,and obtained the proportion of each futures according to the model.However,in the actual investment process,futures are leveraged,which is also one of the biggest characteristics that futures differ from other financial assets.Considering the complexity of futures leverage,previous scholars have not studied the issue of futures portfolio management with leverage.Many experts and scholars only rely on subjective judgment to give the leverage of futures,which not only lacks theoretical support,but also makes investors face enormous risks(forced liquidation),and which greatly deviates from the original intention of futures portfolio management.In addition,all the above studies adopt the buy-and-hold strategy,and assume that the data of returns on each futures are sufficient and can reflect the future.On this basis,scholars have given the investment strategy of the optimal capital ratio for each futures.In fact,the buy-and-hold strategy is a very negative way of investment.It can not make good use of the short-mechanism of futures to gain more returns.Therefore,we use the classic strategy of Dual Thrust instead of buy-and-hold to invest in futures.The performance of investment strategy will be affected by many factors,and many kinds of futures have less historical data,so the historical data of returns of each futures on strategy can not well reflect the future,which need to be given by experts' estimations according to their knowledge and judgements.In view of this,the paper constructs the futures portfolio selection model with leverage.The model solves the problem of capital proportion and optimal leverage once for each futures on strategy.Empirical results show that the futures uncertain portfolio selection model with leverage can better control risks and improve returns.