中文摘要：

提出了允许卖空和不允许卖空2种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．在允许卖空情况下，运用拉格朗日乘数法和Sherman-morrison方程求出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与均值一方差投资组合的有效前沿相同．在不允许卖空情况下，运用不等式组的旋转算法进行求解．该算法避免了通常处理二次规划问题所需的松弛变量、剩余变量和人工变量，因而操作更为简便，计算效率也更高．最后，以1个具体例子比较2种模型，并得到以下结论：在2种情况下，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：

Considering the expected rate of the return of the portfolio and its risk （variance）, the author proposed a maximizing the utility portfolio selection model with risk-free asset,and importantly studied the situation in which the lending and borrowing rates of risk-free asset were different. Under short sales situation,using the Lagrange method and Sherman-morrison＇s equation, the paper gets the optimal investing rate of every security and studies the efficient frontiers＇ character. Under no short sales situa- tion,the paper solves the model by the pivoting algorithm. The algorithm solves the quadric programming problem without adding slack ,surplus and artificial variables. It is very efficient and easy to operate. At last, the paper compares the two models using an example and gets the result that risk preference coefficient with short sales and without short sales could reflect the investor＇s expected rate of return and variance within the entire interval, and risk-free assets can create investment chance.