Portfolio Opitimization Model Based On Fuzzy Analysis

The paper mainly uses the fuzzy theory,possibility theory and linear program-ming to study portfo1io selection problems in the uncertainty environment.First, the liquidity of securities is introduced, and the measure of liquidity is re-viewed in the paper. Based on the uncertainty of liquidity, it is considered as the fuzzyevent. According to the possibility theory, the possibilistic two-goal opitization modelwith fuzzy liquidity constraint in frictional securities market is proposed, meanwhilethe specific example is given.Second, considering the situation which the expected returns rates is difficult topresent precisely, from the point of fuzziness, on every confidencde level, we take thedegree deviated from the central point as the measure of risk. Similar to Markowitz'smean-variance model, we use the weighted possibilistic mean and a dispertion indexto measure the expected returns rates and risk respectively. Based on this, a weightedpossibilistic mean-dispertion portfolio selection model is proposed, and the presenceconditon of the solution of the model is given and the specific example is given toexplain the method's valitidy.At last, fuzzy numbers are also used to describe the expected returns rates, inte-grating the transaction cost, bounded constraints on holdings of assets, especially newadded assets, we propose a possibilistic mean and VaR portfolio adjusting model withnew added assets. Based on possibility theory, the mew model can be transformedinto a linear programming problem and the specific example is adopted to explain themethod's practice.