中文摘要：

利用系数为对称三角形模糊数的模糊AR模型预测投资收益，以模糊收益中值的协方差衡量投资风险，在引入流动性约束的条件下，拓展MARKOWITZ的单期均值方差模型为多期模糊投资规划，每期期末利用改进的清晰化公式将预测的模糊收益转化为清晰的投资收益，构造出一个两步机会规划寻求投资收益和投资风险的Pareto解。采用含遗传交叉变异因子的粒子群算法求解。对上证50指数中的32只股票进行实证分析，并利用离散多期均值一方差模型检验所提出模型的有效性。检验结果表明：两步机会规划模型的最优投资组合的投资收益落在模糊收益值的允许区间之内，且其预测误差较小；在相同投资收益约束条件下，两步机会规划模型可以比多期MV模型承担更低的投资风险。

英文摘要：

Using the fuzzy AR model, of which the coefficient is symmetry fuzzy triangular number to forecast the investment returns, and the covariance of the middle value of the fuzzy return to measure the investment risk, we expand the single-period mean-variance model of Markowitz into multi-period fuzzy investment programming on condition that the liquidity is introduced as the constraint. Translating the forecasting return into the clear investment return by the defuzzifier formula at the end of each phase, we establish a two-phase chance programming in order to look for the Pareto solution of the binary-objective programming, and resolve this programming with the particle swarm algorithms which includes the factor of genetic cross and mutation. To choose 32 stocks of the SSE 50 to make the empirical analysis, and use of the discrete multi-period mean-variance model to prove the validity of the establishing model, the results show that： the investment return obtained according to the optimal portfolio of the two phase chance programming is in the permission interval of the fuzzy return value, and its forecasting error is less; the risk of the two-phase chance programming is much lower than the risk of the multi period MV model on condition than the constraint is the same investment return.