译的不好，，还请见谅。。。
大部分内容来自wiki
decision theory决策理论部分：
Normative and descriptive decision theory
规范和描述性决策理论
规范或规范的决策理论关心的是确定最好的决定(在实践中,有些情况下,“最好”的不一定是最大,最优可能还包括值除了最大,但在特定或近似范围),假设一个理想的决策者充分了解,能够准确无误地计算,完全理性的。这说明性的方法的实际应用(人们应该做出决定)决策分析,旨在发现工具,方法和软件帮助人们做出更好的决策。系统的、全面的软件工具最发达的以这种方式被称为决策支持系统。
What kinds of decisions need a theory?
在什么条件下需要决策？
1.Choice under uncertainty
1.在不确定性条件之下
This area represents the heart of decisiontheory.The procedure now referred to as expected value was known from the17th century.Blaise Pascal invoked it in his famous wager (see below),which is contained in his Pensées, published in 1670.The idea of expectedvalue is that, when faced with a number of actions, each of which could giverise to more than one possible outcome with different probabilities, therational procedure is to identify all possible outcomes, determine their values(positive or negative) and the probabilities that will result from each courseof action, and multiply the two to give an expected value.The action tobe chosen should be the one that gives rise to the highest total expectedvalue.In 1738, Daniel Bernoulli published an influential paper entitledExposition of a New Theory on the Measurement of Risk, in which he uses the St. Petersburg paradox toshow that expected value theory must be normatively wrong.He also givesan example in which a Dutch merchant is trying to decide whether to insure acargo being sent from Amsterdam to St Petersburg in winter,when it is known that there is a 5% chance that the ship and cargo will belost.In his solution, he defines a utility function and computes expectedutility rather than expected financial value (see[2] for a review).
期望值的理念是,当面对大量的行动,每一个都有不同的概率并可能引起多个可能的结果,合理的过程是识别所有可能的结果,确定它们的值(正面或负面)和造成每个行动结果的概率,并增加这两项产生一个预期值。
应该选择的行动是总预期值最高的。在1738年,丹尼尔·伯努利发表一篇有影响力的论文题为博览会上的一个新的理论预测风险,他使用圣彼得堡悖论表明,预期值理论是被错误规范的。他也给了一个例子, 一位荷兰商人试图决定是否在冬天投保货物从阿姆斯特丹发送往圣彼得堡,当他知道有5%的可能性,他的船和货物都将丢失。他在解决方案,定义了一个效用函数和计算期望效用,而不是预期财务值。
效用函数（effectivenessfunction; utility function; utility function used）：效用函数通常用来表示消费者在消费中所获得的效用与所消费的商品组合之间数量关系的函数，以衡量消费者从消费既定的商品组合中所获得满足的程度。
"效用函数" 在工具书中的解释
a、表示消费者在消费中所获得的效用与所消费的商品组合之间数量关系的函数。它被用以衡量消费者从消费既定的商品组合中所获得满足的程度。运用无差异曲线只能分析两种商品的组合,而运用效用函数则能分析更多种商品的组合。其表达式是:U=U(x, y,z, …)式中 x, y, z分别代表消费者所拥有或消费的各种商品的数量,公式左边的U为……
"效用函数" 在学术文献中的解释
b、效用函数的定义是:设f是定义在消费集合X上的偏好关系,如果对于X中任何的x,y,xfy当且仅当u(x)≥u(y),则称函数u:X→R是表示偏好关系f的效用函数
c、F(X)称为效用函数.加权P范数法的关键是权系数的确定.有2种基本的方法,一是老学习法[1,2],该方法依据目标函数的相对重要性来选取权系数
d、一个人的效用应是财富x的函数,这个函数称为效用函数,从理论上来讲,它可以通过一系列心理测试来逼近得到每个人的效用函数.不同的决策者应有不同的效用函数.首先我们寻求效用函数所满足的性质或某些特殊类效用函数所满足的性质
e、这是一种理论假设,他们运用的数学函数式所建立的模型称为“效用函数”.按照这类模型,人都能被假设成为可以决定在每一种可能的时间分配中产生一定的利益水平,并且追求利益最大化的选择
f、—第i种运输方式的费用,有时也称为效用函数,u=ao+alx一+灸xC.丁—第i种运输方式的出行时间.C—第i种运输方式的运输费用
g、为了对控制做出评价,需要一套函数作为评价指 标:J(t)=∑∞k=0kγU(t+k)=U(t)+Jγ(t+1)(2)其中U(t)=U[R(t),A(t),t]用以对每步控制进行评价,称为效 用函数.J(t)函数表示了从此刻开始的每步效用函数值的累积,称为费用函数。
2.Intertemporal choice
2.跨期选择
Intertemporal choice is concerned with thekind of choice where different actions lead to outcomes that are realised atdifferent points in time. If someone received a windfall of several thousanddollars, they could spend it on an expensive holiday, giving them immediatepleasure, or they could invest it in a pension scheme, giving them an income atsome time in the future. What is the optimal thing to do? The answer dependspartly on factors such as the expected ratesof interest and inflation, the person’s lifeexpectancy, and their confidence in the pensions industry. However evenwith all those factors taken into account, human behavior again deviatesgreatly from the predictions of prescriptive decision theory, leading toalternative models in which, for example, objective interest rates are replacedby subjective discount rates.
山不厌高，水不厌深。
