According to the basic characteristics of human’s prospect behavior, this paper bring forward the PD-utility function based on partial distribution, and get the following conclusions:

1) Many results in “prospect theory” from Daniel Kahneman, such as “the utility curve is concave in the profiting field, and is protruding in the losing field”, can be analytically described by the PD-utility function.

2) That the comparison value between losing utility and profiting utility is higher or lower is decided by to prospect level, standard variance of prospect level and realized level. And “losing utility is anyway larger than the profiting utility when the losing sum is equal to profiting sum” can be analytically proved.

3) The actual phenomena of “the higher the expectation is, the more the desponding utility is” can be analytically evaluated.

4) We give out the analytic standard to estimate that the intrinsic moving trend of realized level is reversed or not, and the calculating method of reversing value under the different significance level.

5) We give out the concepts of equilibrium value and focus value of realized level, and the calculating method of them. They can be used for the estimating that the realized level is too higher or lower than the proper value in some period and on the basic meaning.

6) We give out the calculating formula for the optimal value of realized level. By the formula, the optimal value of realized level with its appearing probability could be obtained from average prospect level and the standard variance of it.

7) By use of (4), (16), (17), (18) and (21), we can get the utility results of reversal limit level, focus level and the optimal level of prospect behavior.

In this paper, the foundation that we discuss is that when prospect level is invariable, the higher the realized level is, the higher the profit is. This is applicable to circumstance that one has already hold some kind of assets such as stocks ,etc. but, when did not hold some kind of assets, we may hope the realized level lower, so that we can buy them by lower price. In this case, the lower the realized level is, the higher the latent profit is. For the latter, we can probably adopt with the contrary way discussed in this paper, and no longer discuss here. The textual data source is in the websites:

http://finance.yahoo.com

http://www.stockstar.com.cn

ACKNOWLEDGMENT

The authors are very grateful to Professor Wei-xuan Xu of Chinese Academy of Sciences for paying attention to our researches, and to editor and referees for their arduous work.

Prof. Feng Dai, Prof. Song-tao Wu, Prof. Ya-jun Zhuang

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