英语翻译在上一章,我们主要处理了对数效用最优化的问题.而在当前的关于投资组合优化问题的学术研究中,还有其他一些广泛采用更复杂的效用函数,比如线性效用函数.在这一章,我们主要以

英语翻译在上一章,我们主要处理了对数效用最优化的问题.而在当前的关于投资组合优化问题的学术研究中,还有其他一些广泛采用更复杂的效用函数,比如线性效用函数.在这一章,我们主要以
英语翻译
在上一章,我们主要处理了对数效用最优化的问题.而在当前的关于投资组合优化问题的学术研究中,还有其他一些广泛采用更复杂的效用函数,比如线性效用函数.在这一章,我们主要以指数效用函数为例探讨其他效用函数最优化的问题.
The below sentences are permitted to use by G An for his final project.

英语翻译在上一章,我们主要处理了对数效用最优化的问题.而在当前的关于投资组合优化问题的学术研究中,还有其他一些广泛采用更复杂的效用函数,比如线性效用函数.在这一章,我们主要以
In last chapter,we were talking about log utility.However,there are some other more complexed utility functions adopted widely in the present study and research for investment portforlio optimization,such as linear utility function.In this chapter we will take the exponential utility function as an example to discuss the optimization of other utility functions

In the chapter, we dealt with the effectiveness issue. optimized nesting in the current about investment portfolio to optimize the academic research, and other widespread adoption of more complex utility function, such as linear utility function. in this chapter we mainly index utility function as a

手工翻译：
在上一章，我们主要处理了对数效用最优化的问题。
In the last chapter, we mainly solved logarithmic utility optimization problem
而在当前的关于投资组合优化问题的学术研究中，还有其他一些广泛采用更复杂的效用函数，比如线性效用函数。
And now about investment...

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手工翻译：
在上一章，我们主要处理了对数效用最优化的问题。
In the last chapter, we mainly solved logarithmic utility optimization problem
而在当前的关于投资组合优化问题的学术研究中，还有其他一些广泛采用更复杂的效用函数，比如线性效用函数。
And now about investment optimization problem studying, there are other more complecated and more extensive used utility functions, like linear utility function.
在这一章，我们主要以指数效用函数为例探讨其他效用函数最优化的问题。
in this chapter, we mainly use exponential function to compare with other utility functions about optimization problem
不确定optimization problem是不是最优化问题

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In the chapter, We dealt with the effectiveness issue about logarithm optimization (最优化) And in the current about investment portfolio to optimize the academic research, other widespread adoption of ...

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In the chapter, We dealt with the effectiveness issue about logarithm optimization (最优化) And in the current about investment portfolio to optimize the academic research, other widespread adoption of more complex utility function, such as linear utility function. In this chapter we mainly index utility function as an example to explore other utility function in optimization. 额..差不多了吧

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In last chapter, we were talking about optimization of logarithmic utility. However, there are some other more complexed utility functions adopted widely in the present study and research for investm...

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In last chapter, we were talking about optimization of logarithmic utility. However, there are some other more complexed utility functions adopted widely in the present study and research for investment portforlio optimization, such as linear utility function. In this chapter we will take the exponential utility function as an example to discuss the optimization of other utility functions.

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接下来的句子允许用“G An”（这个我不明白 应该是专业词汇吧或是打错了）作为他最后的课题

In the last chapter, we mainly handle the optimization problem of logarithmic utility. And in the current investment combinatorial optimization problem of academic research, and some other widely adop...

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In the last chapter, we mainly handle the optimization problem of logarithmic utility. And in the current investment combinatorial optimization problem of academic research, and some other widely adopted more complex utility function, such as linear utility function. In this chapter, we mainly index utility function as an example to discuss the other utility function optimization problems.

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In the previous chapter, we have mainly dealt with the logarithm effectiveness optimization issue. But in current about in investment profolio optimization question scholarly research, but also has ot...

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In the previous chapter, we have mainly dealt with the logarithm effectiveness optimization issue. But in current about in investment profolio optimization question scholarly research, but also has other widely to use the more complex utility function, for instance linear utility function. In this chapter, we mainly discuss other utility function optimization take the index utility function as the example the question.

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In the previous chapter, we talk about the optimization of logarithmic utility. But at presentthere are some other widely adopted and more complicated utility functions in academic study on investmen...

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In the previous chapter, we talk about the optimization of logarithmic utility. But at presentthere are some other widely adopted and more complicated utility functions in academic study on investment portforlio optimization, e.g. the linear utility function. In this chapter, we are to discuss the optimization of other utility functions primarily taking the exponential utility function as an example.

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In the last chapter, we mainly deal with the effectiveness of several optimization problems. In the current portfolio optimization problems on academic research, there are other widely used in more co...

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In the last chapter, we mainly deal with the effectiveness of several optimization problems. In the current portfolio optimization problems on academic research, there are other widely used in more complex utility functions, such as linear utility function. In this chapter, our main example of the exponential utility function other utility function optimization problems.

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In the last chapter, we mainly deal with the effectiveness of several optimization problems. In the current portfolio optimization problems on academic research, there are other widely used utility fu...

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In the last chapter, we mainly deal with the effectiveness of several optimization problems. In the current portfolio optimization problems on academic research, there are other widely used utility function is more complex, such as Linear utility function. In this chapter, our main example of the exponential utility function other utility function optimization problems.

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Depend on previous chapter , our problem having handled the logarithmic efficacy optimization's mainly. But in current relative academic research with investment of combinatorial optimization problem,...

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Depend on previous chapter , our problem having handled the logarithmic efficacy optimization's mainly. But in current relative academic research with investment of combinatorial optimization problem, there are still some adopt more complicated efficacy function other broadly, for instance , linear efficacy function. In this, chapter , we once take exponent efficacy function as example mainly discussing the problem that the efficacy function optimizes other most.

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In the last chapter, we mainly deal with the effectiveness of several optimization problems. In the current portfolio optimization problems on academic research, there are other widely used in more co...

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In the last chapter, we mainly deal with the effectiveness of several optimization problems. In the current portfolio optimization problems on academic research, there are other widely used in more complex utility function, such as Linear utility function. In this chapter, our main example of the exponential utility function other utility function optimization problems.
下面的句子是由G允许使用他的最后项目

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同学，你是学精算的吧？