Based on Partial Distribution, we put forward a PD-utility function of prospect behavior for the first time, the profiting utility function and losing utility function. The PD-utility function can reflect sufficiently the human’s risk preferences properties to profiting or losing, describe and bring to light availably the important relations between profiting utility and losing utility, and interpret many conclusions in Daniel Kahneman’s prospect theory in analytic way.

Also we present the concepts and analytic expressions of essential indexes of realized level for prospect behavior, the limit value, the balanced value, and focus value, especially the method of calculating them. The limit level is beneficial to judge the reversal position of reality movement trend, and the latter is beneficial to judge that the focus of current reality is reasonableness or not. And we give out the calculating formula for the optimal value of realized level for prospect with its appearing probability.

Introduction

In recent years and in the international academic field , it becomes an important research trend that behavioral science is crossed and blended consciously to finance , economy and management science. In this respect, the behavior economics is most representative. Daniel Kahneman, the gainer of 2002 Nobel’s prize of economic science, is a representation of economists those who study behavior economics. Using for reference of psychology researches, the researchers of behavior economics dedicate to discuss the psychology mechanism behind human’s economic behavior.

The main point of researches is that economic behavior is controlled not only by the rational profiting, but also by non-rational psychology. Taking as a scale index, the utility is applied primarily to describe the approving degree of human’s subjective attitude, preference, and value preference to something in reality. The utility theory is widely applied in many fields, like management, economics, risk decision, investment analysis etc. The importance of utility theory leaves no room for doubt. The traditional economics think that rational Economic person can estimate every kind of possibility of the future different consequents, and then maximize their expectation utility, but Daniel Kahneman and some other people do a lot of experiments with investigate, and the results enunciate: rational assumption should be doubted.

So they establish the “prospect theory” [1]. Contrasting the experimental results, they find not all of individuals are rational and risk-avoiding [6]-[8]. Also D. Kahneman and some other people discover that human’s decision lie on the difference between outcome and conceivability, instead of the result itself under the uncertain conditions. In other words, when people make a decision, there is usually a consult standard in his mind, and then looks into difference between the outcome and the consult standard.

Comparing with the describing type of “prospect theory” is better than the axiom type of “expectation utility theory” in explaining human’s attitude of detesting losing. Prospect theory can explain the obvious human’s behavior of risk preference that the expectation utility theory could not explain, and make the decision theory of human behavior more perfect under the uncertain conditions. This paper will establish a stochastic model to describe human’s prospect behavior based on the partial distribution (PD)[11],[12], and give out a new kind of utility function. We call it the PD-utility function. By PD-utility function, we can interpret many of human’s decision behavior.

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

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