Portfolio Model And Its Efficiency Evaluation Under Uncertain Environment

With the development of portfolio theory,portfolio theory has become an important part of financial market.In view of the instability of the securities market,the portfolio of securities under uncertain circumstances has become the focus of many research scholars.Uncertainty is a very important factor in the portfolio model.In many uncertain models derived from the framework of mean variance,most of them consider the quantification of the uncertainty of risk and return.These indicators ignore the friction factors such as transaction cost and market liquidity in the actual market.But these will inevitably have a tremendous impact on the trading results in the actual market,making investors in the securities market are likely to face uncertain,inaccurate and ambiguous data.In many of the uncertain models derived from the mean variance framework,most of them consider the quantification of the uncertainty of risk and return,which ignores the actual market.Therefore,this paper considers using interval number and fuzzy number to quantify these indicators,and incorporates transaction cost and market liquidity into the model under uncertain environment,and establishes corresponding uncertain portfolio model to solve them respectively.Finally,the efficiency of the portfolio model is evaluated by the interval DEA model.This research mainly includes four parts:(1)The quadratic programming model of the portfolio of securities portfolios with improved interval acceptability has been studied.Firstly,establish a portfolio model in a random uncertain environment.Secondly,aiming at the objective function of the constructed uncertain portfolio model and the constraint containing uncertainties,an improved interval acceptability and likelihood deterministic transformation method is proposed to solve the model.Finally,through the data experiment of securities,compare with the existing traditional methods.(2)This dissertation studies the generalized interval quadratic programming model of securities portfolio,and secondly considers how to solve the problem of how to explore the optimal value and prepare for taking risks(can reduce risk)for specific models,and then design the algorithm to solve the problem.In this paper,the Lagrangian dual algorithm is used to solve the generalized interval quadratic programming model of the securities portfolio.Based on the duality method,the upper bound of the generalized interval quadratic programming can be used to obtain more accurate values.Finally,through the actual numerical examples of two sets of securities,the generalized interval quadratic programming model for solving the portfolio of securities is explained.The Lagrangian method is used to solve the proposed model to obtain a more accurate risk range of the portfolio,which is helpful to investors.Make more reasonable investment choices in real life.(3)In this dissertation,for the portfolio problem in fuzzy environment,the triangle and trapezoidal fuzzy numbers are used to describe the return and liquidity of securities respectively,and the linear transaction cost is introduced into the model to establish a new investment with transaction cost and liquidity constraints.A fuzzy quadratic programming model with minimized portfolio risk.In order to solve the fuzzy model,this paper proposes to use the cut-set to transform the fuzzy quadratic programming model into interval planning.Finally,through the securities numerical experiment with fuzzy numbers,the model constructed in this paper is compared with the three models that set the existence of liquidity and transaction cost.The experimental results show that the model obtained by this model is better,and investors can get the fuzzy environment.The risk value corresponding to different parameters enables investors to give a reasonable investment closer to the actual market situation.(4)This dissertation combines the two theoretical systems of portfolio and efficiency evaluation.Based on the interval yield and risk loss rate of securities in uncertain environment,the interval DEA method is used to propose the investment efficiency evaluation model of interval DEA,and the efficiency evaluation is carried out.The complex nonlinear problem in the process is transformed into a data-based nonparametric problem.In addition,for the fuzzy yield of securities in uncertain environment,the transaction cost,transaction volume and other constraints are introduced,and the efficiency evaluation model of fuzzy portfolio under different risk measures based on DEA is established.Finally,the validity and practicability of the efficiency evaluation model of this paper are verified by practical application,which is beneficial to investors making reasonable investment decisions on the efficiency of portfolio investment in uncertain environments.