引入成交量变化率的马柯维茨均值方差模型

对马柯维茨的均值方差理论进行了推广，进一步细化原模型中的风险。把成交量变化率的方差也视为一种风险，在收益率的方差中加入成交量变化率的方差，构成一种两者线性组合的新证券组合风险。讨论在给定一定收益率和成交量变化率的条件下使得新风险最小的优化求值问题。把原模型中没有无风险证券时的前沿证券曲线从双曲线（抛物线）推广到双叶双曲面（抛物面），把含有无风险证券时的前沿证券曲线从直线推广到圆锥面，还得到了一系列相应结论。同时对股票投资最优组合选择问题进行实证检验。

Markowitz mean-variance model with vary rate of trading volume

Markowitz mean-variance theory is generalized, and the primary risk is futher refined. The variance of change rate of trading volume is regarded as a new risk. By adding the variance of change rate of trading volume to the variance of return rate,a new stock combination risk is composed by two linear combinations. The new optimization model is minimizing the risk in the condition of given return rate and change rate of trading volume. The frontier portfolio curve is generalized from hyperbola （parabola） to hyperboloid of two sheets （ paraboloid）. When there exists risk securities, the frontier from curve is generalized from straight line to conical surface. Meanwhile, a series of corresponding conclusions are obtained. Finally, the selection problem of optimal combination for stock investment is empirically tested.