Abstract: As investors face the uncertainty of randomness and fuzziness simultaneously in stock market, the paper defines the security returns as random fuzzy variables. Based on the prospect theory and investors’ psychological trait, a random fuzzy portfolio model with different investor risk attitudes is proposed by constructing different random fuzzy returns, target weights and membership functions of expected return. Under the decline and rise stages of stock market, the differences of portfolios for investors with different risk attitudes and the performance of the proposed model are empirically studied. The results show that the risk attitudes of investors can affect the structures of portfolios, and the proposed model is viable in practice and can be used to construct portfolios which meet the need of investors with different risk attitudes.

Key words: financial engineering, portfolio model, random fuzzy number, risk attitude, prospect theory

摘要： 考虑投资者面临证券市场随机和模糊的双重不确定性,把证券收益率视为随机模糊变量。在前景理论下考虑投资者的风险态度,建立不同的随机模糊收益率、期望收益隶属度函数和目标权重,构建考虑投资者风险态度的随机模糊投资组合模型。采用实证方法把市场分为下降和上升两个阶段,研究不同风险态度投资者的投资组合差异及模型表现。结果表明:投资者的风险态度会影响投资组合的结构;考虑投资者风险态度的随机模糊投资组合模型,能够满足不同风险态度投资者对投资收益和风险的差异需求,且在实际投资决策中具有可行性。

关键词: 金融工程, 投资组合模型, 随机模糊数, 风险态度, 前景理论