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中文摘要：
在VaR约束下，以线性加权和法求多目标规划，建立了组合投资的收益最大，同时方差风险最小的组合贷款多目标优化决策模型．该模型的特点是运用了多目标规划的方法建立投资组合优化问题的多目标函数，利用线性加权和法把多目标规划转化为单目标规划，解决了各个商业银行可根据自己的需要选择适合的损失率与收益率，使组合风险最小、其收益最大的最优投资组合问题；同时考虑了风险之间的相关性．通过VaR约束排除了风险相对较高风险的贷款组合，有效地控制了组合风险，使贷款的分配直接反映了商业银行的风险承受能力，并且确立了在多目标组合贷款中的有效集，它在风险和收益的空间上的轨迹也存在着这样的有效边界．
英文摘要：
On the constraint of VaR, this paper uses the multi-objective programming of the linear weighted sum method to build a multi-objective decision function with the maximum return and the minimum risk. The multi-objective programming method was used to build an optimized investment portfolio and the linear weigh- ted sum method was applied to change the multi-objective regulation into the single objective regulation. Thus commercial banks can choose the loss and yield ratio depending on themselves to solve the problem of the minimum risk and the maximum return. The correlation between the risks was considered and the VaR restraint was used to delete the relatively high-risk loan, so the model can effectively control the portfolio risk and make the distribution directively reflect the banks＇ endurable ability to the risk. The efficiency sets of the loan portfolio were set up, which are the similar with the efficient frontier that exists in the trace of the space of risk and return.
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