中文摘要：

提出了在允许卖空情况下含有无风险资产且借贷利率不同的效用最大化的投资组合模型。在允许卖空的情况下，运用拉格朗日乘数法求出了效用最大化投资组合的最优投资策略，并证明了其有效前沿和均值-方差投资组合的有效前沿相同。计算结果表明，风险偏好系数在整个取值范围内都能够较好地反映投资者对收益和风险的选择态度，而且，含无风险资产的借贷拓展了投资机会空间。

英文摘要：

A utility maximization model of the investment portfolio including risk-free asset is put forward, with short sales allowed. Under short sales situation, the optimal investment strategies are obtained by using Lagrange method, and the efficient frontiers＇ character is also studied. The result indicates that risk preference coefficient with short sales allowed reflects the investor＇s expected rate of return and the variance within the entire interval.