摘要随着人民生活水平的提高,人们拥有越来越多的可支配收入，投资的风险与收益问题在现代社会成为一个核心问题，大部分人都会将自己的收入进行投资赚取更多的收益。一个理性的投资者必然想要得到较大的收益，但是我们都知道收益与风险并存，收益越大风险理所应当也会增大，所以收益最大的同时而风险最小是不可能的。但是我们可以通过不同类型的投资组合使得在投资收益和风险中找到一个平衡点，即在一定的风险下获得最大的收益，或者在一定的收益下风险最小。87196

在市场上选择多种投资时，存在风险资产与无风险资产（例如存银行）的选择，在投资组合的策略上要设计考虑两个要求：总收益尽可能大的同时总风险又尽可能的小。但是这两个目标在一定程度上是对立的，因此我们选择建立投资中收益和风险的双目标优化模型。但是由于收益和风险这两个目标是对立的，直接求解非常困难。于是将模型简化为，模型一：在一定收益水平上风险最小；模型二：在一定风险水平下收益最大；模型三：引入风险与收益的权重，我们称之为风险收益系数，求解模型三。

    综合三个模型求解结果，对于问题一我们应当选择风险水平为0。0065，净收益为0。21的投资组合进行投资，即，，，，。（其中为存银行的资产，其余资产为小数，即所投资资产占总投资资产的比例）。对于问题二，我们应当选择风险水平0。074，净收益水平0。3200的投资组合进行投资是=0，=0=0，=0。1255，=0。0414，=0，=0，=0。1081，=0。2097，=0。1432，=0。1797，=0，=0，=0。1575，=0，=0。

毕业论文关键词：投资组合；双目标优化；风险偏好

Abstract With the improvement of people's living standards and growing disposable income, investment risk and return issues in modern society is playing an increasingly important role, most people will invest their earnings earn more income。 A rational investor will inevitably want to get big gains。 But we all know that not all eggs in one basket truth, earnings and risks, benefits the greater the risk will increase as it should be, so in order to be able to make the greatest profits at the same time minimize the risk is impossible。 But we can make different types of portfolio investment income and risks found in a balance, that is, in a certain risk to get the maximum benefit, or at a certain minimum income risk。

The importance of investment income and risk model is self-evident, we believe that investment-related knowledge through learning can make themselves more aware of their role in the direction of investment。

When selecting a variety of investment in the market, there is a risk assets and risk-free assets (such as bank deposits) options on portfolio strategy designed to consider two requirements: total revenue as large as possible while total risk small, but two goals to some extent contradictory。 So we choose to create a double target investment return and risk optimization model。 However, due to the benefits and risks of these two opposing goal, direct solution is very difficult。 So the simplified model, a model: at a certain minimum level of income risk; Model II: at a certain level of risk the largest gains; model Third, the risks and benefits of the introduction of the right weight, which we call risk-benefit factor, solve the model III。

Integrated three model results,for a question that we should choose the level of risk was 0。0065, 0。21 net income of portfolio investment, that is,，，，， (where asset bank deposit and the remaining assets of the decimal, ie the proportion of total investment assets on investment)。 For question two, we should choose the level of risk 0。074, 0。32 net level of portfolio investments=0，=0=0，=0。1255，=0。0414，=0，=0，=0。1081，=0。2097，=0。1432，=0。1797，=0，=0，=0。1575，=0，=0。