中文摘要：

采用隶属度消除期货和现货收益率的异常波动对套期保值的影响，用非线性风险叠加原理描述多种期货对一种现货的组合风险，在最小方差套期保值模型的基础上，建立了基于最小模糊方差的最优交叉套期保值模型。本模型的创新与特色一是通过多种期货对一种现货的交叉套期保值提高了套期保值的有效性。这解决了仅用一种期货对一种现货进行交叉套期保值而导致风险较大的问题。二是用隶属函数对期货和现货收益率赋权消除离散程度大的收益率对最优套期比的影响。在采用隶属函数赋权的情况下，离散程度大的期货和现货收益率会被自动地赋予较小的权重，有效地减小了异常数据对最优套期比的影响。三是用非线性风险对冲原理叠加多种期货对一种现货的组合风险。通过期货与现货收益率的模糊协方差矩阵计算组合风险，反映了风险的非线性叠加和非线性对冲。四是现有研究的多种期货对一种现货的最小方差交叉套期保值模型仅仅是本模型在模糊隶属函数取1时的一个特例。当本模型的隶属函数为1时，本模型就是多种期货对一种现货的最小方差交叉套期保值模型；当本模型的隶属函数为1时、且研究对象为一种期货对一种现货套期保值时，本模型就是一种期货对一种现货的最小方差交叉套期保值模型。通过实证研究和与现有研究的对比分析，证明本研究所建立的模型可以有效的减小套期保值的风险并提高套期保值的有效性。

英文摘要：

This paper put forward a minimum fuzzy-variance optimal cross hedging model on the basis of MV hedging model. The influence of abnormal fluctuation of futures and spot＇s yield to hedging is eliminated by using subjection of fuzzy. Combination risk of multi-futures to single cash is described by the nonlinear principle of superposition. The contribution of the model is firstly that we use cross hedging of multi-futures to single cash to enhance the efficiency of hedging. This solves the poor risk problem rising from one-futures to hedge single cash. Secondly, we weigh the futures and cash yield with membership function to eliminate the influence of discrete big yield on optimal hedging ratio. When the futures and cash yield is abnormal, the membership degree is little. Then the influence of abnormal date on the optimal hedge ratio is much reduced. Thirdly, we superpose the multi- futures to single cash combination risk by use of the nonlinear hedging principle. The combination risk is calculat- ed by the fuzzy matrix of futures and spot＇s yield, which reflect the nonlinear superposition and nonlinear hedging. Fourthly, the hedging model of multi-futures to single cash based on the returns variance minimum is one example of our model while the subjection of fuzzy is equal to one in this paper. When the research object is the hedging of one-futures to single cash, this model is cross hedging model of one-futures to single cash based on the returns variance minimum while the subjection of fuzzy is equal to one. By comparative analysis, Cross hedging model based on minimum fuzzy-variance can effectively reduce the risk of hedging and enhance the effective of hedging.