具有VaR约束的不相关资产可能性投资组合模型及算法

Possibilistic portfolio model for uncorrelated assets with VaR constraint and its Algorithm

利用模糊可能性均值和方差的概念,假设资产的收益率为模糊数时,提出具有VaR约束的不相关资产可能性投资组合模型.该模型更好地反映了在非随机因素影响的金融市场下,具有风险厌恶特征的投资者不仅要求投资组合的实际收益率能够达到给定的期望收益率,同时也能够以较大的可能性保证未来遭受的最大可能损失不超过某一值.当证券收益率服从模糊正态分布时,给出了该模糊可能性投资组合模型的有效投资比例的解析形式,同时给出了可能性有效前沿.最后选取上海证券交易所不同行业的部分股票进行了实证分析.结果表明,该模型不仅能够更好地反映现实经济环境中影响资产投资收益的模糊不清晰因素,而且在VaR约束下,投资者能够选择更适合自己的投资组合.

Based on fuzzy possibilistic mean and variance, a possibilistic portfolio model for uncorrelated assets with VaR constraint was proposed while return on assets is fuzzy number. The model shows more clearly that, in the financial market affected by non- random factors, risk-averse investors wish not only to reach the expected rate of returns in their actual investment, but also to assure maximum possible for future maximum loss is lower than a certain value. Under the condition of that securities yields obediences fuzzy normal distribution, the formula for effective investment ratio of fuzzy possibilistic portfolios model was derived, possibilistic efficient frontier was also given. Finally, an empirical study is carried out by using some stocks data of various industries listed at the Shanghai Stock Exchange. Conclusion shows that the model not only reflects uncertain factors affected asset investment income in reality of the economic environment, but also helps investors to choose more suitablea portfolio under the VaR constraint.