中文摘要：

投资者进行投资实践时无不面临着背景风险。绝大多数以均值方差为框架的投资组合并没有考虑背景风险，其效用在实际应用中容易受到背景风险的影响。本文在含有交易费用的双目标函数模型中引入背景风险，从是否含有背景风险和背景风险偏好度大小两方面对投资组合问题展开研究，并使用智能算法得到模型的最优解，对模型进行实证分析。实证结果表明：1）当背景风险收益为0时，含有背景风险的投资组合比不含有背景风险的投资组合更能反映真实的投资环境。2）当背景风险收益不为0时，含有背景风险的投资组合比不含有背景风险的投资组合得到更高的收益。因此，考虑背景风险后投资组合的构建优于不考虑背景风险投资组合的构建。

英文摘要：

In practice, the investors always face the background risk. Most of the M-V framework in portfolio selection problems does not take it into account, so the utility of portfolio is influenced by the background risk. This article proposes a bi-objective portfolio selection model with background risk and transaction costs to study how background risk affects the utility and how background risk preference affects it. Then we introduce an improved genetic algorithm to solve this model. Finally, we use the collect data to test the performance of the model to the portfolio selection problem. Based on the empirical study, we make conclusions that when the expected return of background risk is zero, the model with background risk can better reflect the investment risk of the real economic environment ; when the expected return of background risk is not zero, the model with back- ground risk can yield more return. Thus, the model with background risk is superior to the model without it.