Prospect Theory An Analysis of Decision under risk

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前景理论及其价值函数与权重函数研究述评

前景理论及其价值函数与权重函数研究述评
风险偏好的分解:价值函数和权重函数
为叙述方便,本文将前景理论(prospect theory,pt)和累积前景理论(cumulative prospect theory,cpt)统称为前景理论,只有当区分这两种理论时,才使用pt和cpt。本文对有关学者基于前景理论的价值函数和权重函数及其参数估计的有关研究进行简要述评。
2.其它形式的价值函数表达式。rieger(2007)在研究中发现,经典的前景理论的价值函数不能描述简单抽奖中的非常风险厌恶(very risk-averse)问题。于是其提出了另外一种价值函数表达式,并很好地解决了这一问题。其价值函数表达式如下:(9)
其中,α∈(0,∞),β∈(0,∞)
另外,在本篇文献中,作者还提到了另外一种价值函数的表达式:
gonzalez & wu(1999)指出,可以用两个参数来刻画权重函数:用参数“辨别力”(discriminability)来刻画权重函数曲线的曲率(curvature);用参数“吸引力”(attractiveness)来刻画权重函数曲线的仰角(elevation)。并给出了如下的权重函数表达式:
(17)
其中,p为权重函数曲线与45度线的交叉点处的概率。
价值函数和权重函数参数估计研究
(一)价值函数参数估计研究
camerer & ho(1994)通过对9名学生的调查,得出了α=0.32。wu & gonzalez(1996)对kahneman & tversky给出的函数进行回归,得出α= 0.52。同时他们对prelec的价值函数形式进行了回归,并得出了α=0.48的结论。gonzalez & wu(2003)分别设计了两结果(two-outcome)和三结果(three-outcome)的抽奖(gamble)。对于两结果的抽奖,他们对kahneman & tversky的价值函数进行回归,结果得出α=0.49(中值);对于三结果的抽奖,结果得出α= 0.23。

前景理论及其应用

前景理论及其应用

前景理论及其应用作者:张迎春来源:《消费导刊·理论版》2008年第16期[摘要]前景理论把心理学研究和经济学研究有效地结合起来,揭示了在不确定性条件下的决策机制,开拓了一个全新的研究领域。

本文介绍了前景理论产生背景,前景理论的三个基本原理、价值函数等,以及前景理论在证券投资、生活中的应用。

[关键词]前景理论效用函数证券投资应用作者简介:张迎春(1971-),女,浙江大学行为与心理系在职硕士,助理研究员。

一、卡尼曼及前景理论卡尼曼(Daniel Kahneman)与特韦尔斯基(Amos Tversky)把心理学运用到现代经济学最成功的方面是前景理论(即展望理论)(Prospect Theory)。

行为经济学代表人物第三十四届诺贝尔获奖者丹尼尔·卡尼曼,卡尼曼教授等人的行为经济学研究从实证出发,从人自身的心理特质、行为特征出发,去揭示影响选择行为的非理性心理因素。

行为经济学强调,人们的行为不仅受到利益的驱使,而且还受到多种心理因素的影响。

卡尼曼等人开创了利用实验研究个体决策行为的先河,人在不确定条件下的决策,似乎取决于结果与设想的差距而不是结果本身。

换言之,人们在决策中,通常会在心里有个参考标准,然后看结果与这个参考标准的差别是多少。

卡尼曼和特维尔斯基发展了“前景理论”,认为它与期望效用理论是互补的。

效用理论(Utility Theory)可用于理性行为;“预期理论”则用于描述实际行为。

风险理论演变经过了三阶段:从最早的期望值理论(Expected Value Theory),到后来的期望效用理论(Expected Utility Theory),到最新的前景理论(Prospect Theory),其中前景理论是一个最有力的描述性理论。

前景理论有以下三个基本原理:(a)大多数人在面临获得的时候是风险规避的;(b)大多数人在面临损失的时候是风险偏爱的;(c)人们对损失比对获得更敏感。

报童模型

报童模型

缺货损失厌恶的报童问题摘要:报童问题是随机存贮管理的基本问题之一。

在预期理论的框架下,我们通过引入损失厌恶参数,基于损失期望最小原则,对经典的报童问题进行了重新思考,给出了缺货损失厌恶的报童的最优定货量的计算公式及订购量与期望损失关系的数学模型.关键词:存贮管理;预期理论;期望损失1、引言不确定性决策一直都是决策理论的基本问题之一。

报童问题是随机存贮理论的基本模型之一,国内外关于报童问题的研究已有很长一段时间,人们也从不同的角度得出了一些令大家可接受且比较满意的方案和数学模型。

如Tsan rt.al[1]提出报童问题的均值方差模型,并且得出如果报童可能最大化期望利润,使得利润方差受到限制,那么其最佳订购量总是小于经典报童问题的订购量;Schweitzer, Cachon[2] 提出效用最大化的报童问题,且得出基于偏爱的不同而有不同的效用函数,(这些偏爱对报童的决策进程有着重要影响);Eeckhoudt et.al[5]研究了风险及风险厌恶对报童问题的效应;Porteus[5]通过对敏感度的定量分析,研究了带风险效用和风险厌恶的报童问题;文平[6]关于损失厌恶的报童—预期理论下的报童问题新解一文,基于Kahneman 和Tversky[6]于1979年提出的预期理论,也得出了比较理想的模型。

然而他们中的多数都是从获利期望值最大和期望效用理论的角度来考察的。

但是,报童问题也是一种经典的单阶段存贮问题。

对报童而言,他每一天的报纸都有三种结果:报纸卖不完、不够卖、刚好够卖。

这三种结局只有最后一种情况下才能达到报童的最大利润,因为报童的最大利润是订购量刚好和市场需求一致,即刚好够卖,也刚好卖完。

在过去关于报童问题的种种模型中,都很少考虑到报纸不够卖,即脱销的情况,此时大多是以刚好满足市场需求的情况来处理。

其实不然,对于这类薄利多销的报童问题而言,他们都不希望自己是做保本生意,都希望充分利用好市场,最大限度地获取利润。

前景理论分绍

前景理论分绍

前景理论坎内曼(D.Kahneman)和特维尔斯基(ersky)等人通过大量精心设计的社会学、心理学实验识别出这些经验规则的原理,发现以这些经验规则为主要特征的直观推断会产生严重的系统性错误和偏差,据此,他们提出了前景理论(prospect theory)。

“Prospect theor y:An analysis of decision under risk",Econometrica,47(2): 263-291 1979? 是他们的原文一、前景理论的理论基础1. 相似性(representativeness)偏差。

人们通常以A与B的相似性为依据,通过事件A的相关数据和信息评估事件B。

2. 可利用性(availability)偏差。

人受记忆能力或知识的局限,在预测和决策时大多利用自己熟悉的或能够凭想象构造得到的信息,但这只是应该被利用的信息的一部分,还有大量的其它的必须考虑的信息对正确评估和决策有重要影响,但人的直觉推断却忽视了这些因素因而出现偏差。

3. 锚链(anchoring)效应与调整。

在多数情况下,对一特定对象做出评估或预测通常会选定一个参考点或起始点。

在评估过程中,人对参考点的选择和调整经常是不充分的,不同的参考点得出的结论不一样,这种由于参考点的不同引起的暂时的反应不足和决策偏差称为锚链效应。

锚链效应在复杂事件的风险评估过程中尤其显著。

4. 认知分歧与群体影响。

人们在面对两种相互矛盾的观点时,持有非主流观点的人与群体之间或多或少有不协调和不适的感觉,人们通常会想办法、找证据支持主流观点,或为了得到群体的认同而倾向于放弃非主流观点,由此产生了认识偏差。

行为心理学家通过大量实验研究发现人的决策并非都是理性的,其风险态度和行为经常会偏离传统经济理论的最优行为模式假设,并得出结论认为人在决策过程中不仅存在直觉偏差,还存在框架依赖偏差(frame dependence biases),经常会在不同的时候对同一问题做出不同的相互矛盾的选择。

浅析经济学的几种研究方法

浅析经济学的几种研究方法

浅析经济学的几种研究方法摘要:目前,经济学理论方面的纷争不仅仅在于观点和问题的不同,而且在研究同一问题的方法上也是各持己见。

经济学究竟是实证的还是规范的一直是经济学界争论不休的问题,相应的实证研究和规范研究则是经济研究中经常出现的两种研究方法;经验研究和理论研究是经济学研究方法的另一种分类;而实验研究则是近几十年来经济学界新出现的研究方法。

了解经济学研究方法对我们理解经济学体系有指导方向的作用,也有利于我们用类似的研究方法解读当前现实中的经济问题,更有利于经济学研究方法上的再创新。

关键字:实证研究规范研究经验研究理论研究实验研究一、引言方法论是一种以解决问题为目标的体系或系统,通常涉及对问题阶段、任务、工具、方法技巧的论述。

方法论会对一系列具体的方法进行分析研究、系统总结并最终提出较为一般性的原则。

研究方法是任何一门学科的重要组成部分,它提供了人们在该学科领域内分析问题的视角、工具和分析框架,同时它也是不同学科之间相互渗透和相互借鉴的桥梁。

正如任何一门学科都需要有自己独特的方法论一样,经济学的发展也从来没有离开研究方法的嬗变而独立进行。

以往的200多年间,研究方法的科学性是评价经济学家智力高低及其观点正确与否的主要标志。

19世纪门格尔和施穆勒之间的“方法论之争”是经济学史上一次最重要的方法论之争。

萨缪尔森的“描述法”和弗里德曼的“工具主义”亦是如此。

直至今日,诸如规范的研究方法和实证的研究方法之间的争论依然没有停止。

而研究方法的层出不穷将会导致一些列的问题。

本文就目前经济领域较为广泛使用的三组研究方法及其争论焦点作一简单的介绍。

二、实证研究和规范研究经济学的研究方法一般分为规范研究方法和实证研究方法两种,相应的经济学也分成规范经济学和实证经济学。

根据新帕尔格雷夫大辞典的定义,实证经济学是经济学中对经济现象进行描述与解释的一个分支;,其目的是就实际问题,包括公共政策问题而提出。

而规范经济学的内容则致力于对实证经济学的应用建议。

行为金融理论综述ppt

行为金融理论综述ppt

Froot and Dabora 1999
Kaul, Mehrotra and Morck2000 Lamont and Thaler 2002 Wurgler, J., Zhuravskaya, 2002
理论解释
基本面风险
Barberis 和 Thaler( 2003)
— 很难找到两种有定价差异的完美替代物
vs. highest value of prospects
final wealth vs. change in wealth the magnitude of change (+/-) from reference point – Kink at the origin: Concave vs. concave/convex – Steeper for losses than for gains
π (0) =0, π (1) =1 π (p)>p for small p
π (p)<p for all 0<p<1
thus, π (p)+π (1-p)<1
心理账户 Mental accounting (MA)
对信息处理的三种方式 – a minimal account (examine only the difference) – Sunk cost effect
前景理论 Prospect theory
权重方程 the weighting function
π is an increasing function of p
π (0) =0, π (1) =1 π (p)>p for small p
π (p)<p for all 0<p<1

组织行为学-第六章决策行为

组织行为学-第六章决策行为
*
衡量指标
个体决策
群体决策
速度


正确性
较差
较好
创造性
较大
较小
冒险性
因个人的个性、经历而异
若群体成员特别是领导者富有冒险性,则趋于冒险性;反之则反是。
*
群体决策 个体决策和群体决策对比
群体决策的优势 提供更多的有用信息和知识。 提出更多的候选方案。 提高对最终解决方案的接受程度。 提高决策的合法性。 群体决策的不足 时间较长。 屈服群体压力。 受少数人的左右。 责任不清。
*
*
合理性的概念 实践层次上的合理性 形式层次上的合理性 价值层次上的合理性 认识层次上的合理性 制约合理性的主要因素 感情因素 价值取向 信息为前提 过多的费用 习惯和记忆 组织的惯性 组织中的权力作用
决策的法则 代表性法则 可利用性法则 锚定和调整法则 决策策略 格兰多里(A.Grandori)的决策策略规定性理论观点。决策策略是一个从最优到随机的策略的一个连续体,依不确定程度和利益冲突条件的不同,而存在一个恰当的策略。 决策的最优策略 决策的满意策略 决策的行动策略 决策的直觉策略
*
情境游戏
Hunting!!
让我们打猎去!
*
游戏规则
u分为两组 u每组选出1位领导者,5位幕僚 n由领导者发号施令,幕僚只提供意见 u每组再选出10个人当动物棋(猎人X1、狮X2、鹰X3、蛇X4、鼠X5 ) n棋子只负责行动,不可提供意见 u剩下的人为观察者,在一旁观察 n观察者观察整个游戏进行,不得提供意见
*
A/Q型。这类决策是与下级的个人利益密切相关,但与组织的利益无重大影响的决策。 Q/A型。这类问题与组织利益关系密切,而与下级的利益无直接联系。 Q/AQ型。这类问题与下级利益和组织利益都关系不大,因此对决策质量和下级认可水平要求都不高。 AQ/Q型。这类问题既与组织利益密切相关,又与下级的利益密切相关,因此它具有高质量、高认可的性质。

非对称货币政策效应

非对称货币政策效应

非对称货币政策效应【摘要】文章通过行为金融学中前景理论的视角探讨非对称货币政策。

结果表明不同的货币政策下,收入水平和边际利得的不同会促使人们相应地调整参考点和权重,使总价值函数处于不同的位置使人们呈现出不同的风险偏好,并采取不同的应对措施,从而导致了货币政策的非对称性。

【关键词】前景理论货币政策非对称性价值函数一、前景理论的基本内容(一)决策者的风险决策过程kahneman和tversky(1979)将个人风险条件下的决策过程分为两个阶段,分别是编辑阶段和评估阶段。

编辑阶段是人们在一定的心理活动指导下,按照某种标准用规定的方式对所面对的选项进行描述,从而为之后的评估和选择做简化处理。

评估阶段就是决策者对前期编辑阶段处理后的信息,进行评估并选择的过程。

这一阶段决策者以来价值函数和权函数这两个主观度量函数对信息予以判断。

(二)三个核心概念实际上,前景理论主要围绕值函数、权函数、参照点这三个核心概念展开的。

这三个概念贯穿于决策者风险决策的两个阶段中。

1.价值函数价值函数是决策者对与利得(或损失)相对与参考点变化带来的效用的主观评价。

kahneman和tversky给出的价值函数形式为指数函数。

它具有三方面的特点。

第一,价值的载体不再是收益或损失的最终状态,而是以对参照点的偏离为判断标准,呈反射形状;第二,价值函数在收益区是凹的,体现决策者对收益的风险厌恶态度,而价值函数在损失区则是凸的,体现决策者对损失的风险偏好态度,第三,价值函数表现为对同样数额的收益和损失,收益带来的快乐总是无法抵补损失带来的痛苦的。

2.权函数权函数是评估过程第二个重要的主观函数,虽然随机事件发生的概率总是存在一个客观概率,但是决策者在面对随机事件时,并不完全基于对客观情境的分析得出准确的客观概率,而是常常基于自身的经验和希望进行判断,因此主观概率与客观概率常常不相符。

前景理论中,每一价值函数都被乘以一个决策权重,决策权重本身并不是客观概率,它只是客观概率的一个非线性函数。

对现状偏差效应的综述

对现状偏差效应的综述

对现状偏差效应的综述彭婷婷(西南民族大学社心学院,成都,610225)摘要:安于现状偏差是指个体在决策时,倾向于不作为、维持当前或者以前的决策的一种现象。

目前研究者对这一现象的解释主要有两种:损失规避与后悔理论。

而影响这种偏差的有多种因素,如个体情绪、认知等。

安于现状偏差对销售、投资、管理等领域有着重要的价值。

关键词:安于现状偏差;决策;后悔1.现状偏差效应的历史发展安于现状偏差是指个体在决策时,倾向于不作为、维持当前或者以前的决策的一种现象。

根据现状的来源, 安于现状偏差可以分为两类: 外源的安于现状偏差和内源的安于现状偏差。

外源的安于现状偏差的表现主要是不作为或者维持当前的决策, 而内源的安于现状偏差的表现主要是维持过去的选择。

(Samuelson和Zeckhauser (1988)首次提出安于现状偏差这一概念, 并在实验室实验和现场实验中证实这一决策偏差的存在。

在研究中,被试被要求在一个假想的决策情境的两种版本中(中立版本与现状版本)进行选择。

研究发现,被试倾向于选择现状选项。

另外, 他们在水资源分配、办公室迁移、职业选择等决策情境中都证实了安于现状偏差的存在。

与现实中我们对现状的理性偏好不同, 安于现状偏差在没有转变成本与不确定性影响的决策情境中仍然存在, 是一种非理性的决策偏差。

然而,这种决策偏差在在决策情景中非常普遍。

2.安于现状的心理机制2.1 损失规避损失规避是预期理论(Kahneman & Tversky, 1979)的一个核心概念,是指损失比等量获得所产生的心理感受更加强烈。

安于现状偏差是损失规避的外在行为表现(Kahneman et al., 1991; 刘欢, 梁竹苑, 李纾,2009)。

个体面临现状选项与其他选项时, 现状往往被看作一个参照点, 此时, 相对于改变现状所获得的收益, 个体对改变现状所产生的等量损失赋予更大的心理权重, 因而更倾向于不作为、维持当前或以前的选择(Samuelson & Zeckhauser,1988; Ritov & Baron, 1992; Anderson, 2003)。

沉没成本的机制

沉没成本的机制

沉没成本的机制全文共四篇示例,供读者参考第一篇示例:沉没成本是一个经济学概念,指的是投资者在决策当中会考虑到已经花费的成本,即使这些成本无法收回或是不再具有实际价值。

当人们做出决策的时候,他们会不自觉地将已经付出的成本考虑在内,而不是只考虑未来的投资回报。

沉没成本是一个常见的心理偏差,因为人们往往倾向于认为已经投入的资源是不可逆的,因此他们会继续投入更多的资源,以期望弥补之前的损失。

这种做法常常导致更大的损失,因为决策者并未真正考虑到未来的回报和成本。

沉没成本的机制是指人们在考虑决策的时候,会倾向于考虑已经付出的成本,而不是未来的成本和回报。

这种偏见可能导致人们做出错误的决策,因为他们过于依赖过去的投入,而忽视了未来的风险和机会。

沉没成本的机制在许多领域都有体现,特别是在企业经营和个人投资当中。

企业往往会因为已经投资了大量的资金和资源而继续推进一个不符合预期的项目,而不愿意面对失败。

个人投资者也会因为已经投入大量的时间和金钱而继续持有不良投资,而不愿意承认错误。

为了避免沉没成本的机制对决策的影响,人们可以采取一些策略。

要意识到已经付出的成本是不可挽回的,不应该成为决策的考量因素。

要将已付出的成本和未来的回报相对独立地考虑,以确保决策是基于未来的潜在收益和成本。

人们还可以采取一些行为经济学的方法来消除沉没成本的影响。

通过多角度思考问题,避免陷入认知固执的思维模式。

还可以寻求外部的意见和建议,以获得客观的反馈,避免过于依赖自己的主观看法。

第二篇示例:沉没成本,又称沉没成本效应,是指企业已经发生但无法收回的成本,也称为遗留成本或已付成本。

在决策中,沉没成本通常是不应该影响最终决策的因素,因为它们已经发生,并且无法挽回。

在现实中,沉没成本往往会对人们的决策产生影响,导致他们继续投入资源并做出不理性的决策。

沉没成本的概念最早由经济学家斯斯拉特利(Armen A. Alchian)和阿勒尔(William R. Allen)提出,他们认为沉没成本会影响人们的决策,导致他们继续投入资源去弥补已经失去的成本,而实际上这并不明智。

企业理论:公司如何决策

企业理论:公司如何决策

企业理论:公司如何决策在现代商业环境中,企业决策是一个至关重要的过程。

无论是制定战略计划、投资决策还是日常运营管理,公司的决策都直接影响着企业的发展和成果。

因此,了解和掌握有效的决策方法和理论对于企业的成功至关重要。

本文将介绍一些常见的企业决策理论和方法,并探讨它们在实际应用中的优势和局限性。

1. 理性决策模型理性决策模型是一种基于分析和逻辑推理的决策方法。

它假设决策者具有完全信息、明确目标并能够评估各种选择的后果。

在这种模型中,决策者通过收集和分析数据、评估风险和回报,并选择最佳的决策方案。

然而,现实世界往往存在信息不完全、目标模糊以及风险难以评估等问题。

因此,理性决策模型在实际应用中可能会受到限制。

此外,由于时间和资源的限制,完全分析所有可能的选择也是不切实际的。

因此,理性决策模型往往需要与其他决策方法结合使用。

2. 行为决策模型行为决策模型关注决策者在实际决策过程中的行为和心理因素。

它认为人类决策者在面对复杂问题时往往受到认知偏差、情绪影响和社会压力等因素的影响。

因此,行为决策模型试图解释和预测人类决策者的行为,并提供相应的决策支持。

行为决策模型通过研究人类行为和心理学原理,揭示了许多常见的认知偏差和错误判断。

例如,过度自信、避免损失和群体思维等现象都可能导致不理性的决策结果。

了解这些偏差可以帮助企业决策者更好地识别和纠正自己的错误判断,提高决策质量。

3. 群体决策模型群体决策模型是一种将多个决策者的意见和观点整合起来进行决策的方法。

它认为通过集思广益,可以获得更全面、准确的信息,并减少个体决策者的偏见和错误。

群体决策模型可以采用不同的决策方法,如投票、协商和共识等。

它可以促进团队合作和沟通,提高决策的可接受性和可执行性。

然而,群体决策也可能面临一些挑战,如意见分歧、权力斗争和决策过程的复杂性等。

因此,在实际应用中,需要合理设计和管理群体决策过程,以确保其有效性和效率。

4. 情景决策模型情景决策模型是一种基于特定情境和环境因素进行决策的方法。

确定效应总结报告范文(3篇)

确定效应总结报告范文(3篇)

第1篇一、引言确定效应(Certainty Effect),也称为确定性偏误,是行为经济学中的一个重要概念。

它描述了人们在面对不确定性决策时,往往会高估确定结果的效用,而低估不确定结果的效用。

这一现象在金融市场、保险决策、消费者行为等领域均有广泛的应用。

本报告旨在总结确定效应的相关研究,分析其产生的原因、影响及其在实践中的应用。

二、确定效应的定义与特征1. 定义确定效应是指个体在面对不确定性选择时,倾向于选择确定结果,即使该结果可能不如不确定结果具有更高的期望效用。

2. 特征(1)高估确定结果的效用:个体在面临确定性选择时,往往对其效用估计过高。

(2)低估不确定结果的效用:个体在面临不确定性选择时,往往对其效用估计过低。

(3)风险规避:确定效应导致个体在面临风险时倾向于规避。

三、确定效应产生的原因1. 生物学基础(1)人类大脑对确定结果的偏好:大脑在进化过程中,为了提高生存率,对确定结果产生了偏好。

(2)认知偏差:大脑在处理信息时,会倾向于关注确定性信息,忽略不确定性信息。

2. 心理学基础(1)损失厌恶:个体对损失的厌恶程度高于对收益的喜爱程度。

(2)锚定效应:个体在决策过程中,会受到初始信息的影响,即使该信息与实际情况无关。

3. 社会文化基础(1)社会期望:个体在社会中受到各种期望的影响,倾向于选择符合社会期望的结果。

(2)文化背景:不同文化背景下,人们对确定性和不确定性的认知存在差异。

四、确定效应的影响1. 金融市场(1)资产定价:确定效应导致投资者对确定结果的资产定价过高,对不确定结果的资产定价过低。

(2)投资决策:确定效应导致投资者在投资决策中倾向于规避风险。

2. 保险市场(1)保险产品设计:确定效应导致保险产品设计偏向于确定结果。

(2)消费者行为:确定效应导致消费者在购买保险时,更倾向于选择确定性的保险产品。

3. 消费者行为(1)产品选择:确定效应导致消费者在产品选择中倾向于选择确定性的产品。

沉没成本为什么会影响投资决策

沉没成本为什么会影响投资决策

沉没成本为什么会影响投资决策邵希娟按照现代财务理论的规范性分析,沉没成本不应该影响人们的决策;但根据我们的实际观察以及行为公司理财的实证研究得出:在现实生活中,沉没成本往往严重影响人们的决策!这就是所谓的“沉没成本效应”。

为什么会出现这样的现象?在什么情况下这种现象更加显著?本文利用2002年获得诺贝尔经济学奖的卡尼曼(Kahneman)教授等行为决策学家的理论就这些方面进行分析,并为企业提出相应的防范对策。

一、沉没成本不应该影响决策沉没成本是指决策时已经发生的成本,它涉及到的现金流是已经流出或将肯定流出的现金流,并不因决策后所选取的方案不同而变化。

即:对于决策,沉没成本不是增量现金流。

例1:某公司正在考虑是否投资建一个厂房用于生产一种新的产品,由于公司内部决策层在这件事情上意见不一致,部分人赞成,而另一部分人反对,为此公司聘请某咨询公司为其做可行性分析,以作为该项目决策的主要参考。

双方协定咨询费10万元,咨询开始时付4万元,完成可行性分析报告并通过公司验收后10天内付余下的6万元。

如果该咨询公司的报告客观科学,一旦通过验收,无论最终是投资这个项目还是放弃这个投资,这10万元都要支付,因此这10万元对于该项目决策来说就是沉没成本,因为它不是增量现金流,在接下来的决策中一定要忽略它。

尽管6万元还没有付,但按双方协定是一定要付的;尽管这10万元是为该项目投资决策服务所发生的。

现代财务管理理论明确指出:只有增量现金流是与投资决策相关的[1]。

因此沉没成本不应该影响接受还是拒绝一个项目的决策,它们应该被忽略,所有的财务管理教材在介绍长期投资决策理论时都强调这一点。

二、现实中沉没成本往往严重影响决策国外的研究者做了大量实证研究发现:现实中沉没成本往往严重影响决策(沉没成本效应)。

奚恺元教授对美国和中国的EMBA学员做了类似例2的测试,结果是:那些被试的企业老总们绝大多数的回答是“坚持继续投资”[2]。

例2:你是一家医药公司的总裁,正在进行一个止痛药的开发项目,项目启动了很久,已经投入了500万,再投资50万产品就可以正式上市了。

禀赋效应的相关著作

禀赋效应的相关著作

禀赋效应的相关著作"禀赋效应"是行为经济学中的一个重要概念,指的是个体对于自己拥有的东西赋予的价值高于他们没有拥有的东西。

这一概念最早由心理学家和经济学家提出,并在许多实证研究中得到验证。

以下是一些与禀赋效应相关的经典著作:1."Prospect Theory: An Analysis of Decision under Risk"(《前景理论:风险决策分析》)•作者:Daniel Kahneman和Amos Tversky•这篇经典论文提出了前景理论,其中包含了禀赋效应的概念,对人们在决策过程中对于损失和收益的不对称处理进行了深入研究。

2."Endowment Effect in the Labor Market: Evidence from aField Experiment"•作者:John A. List•这是一项关于禀赋效应在劳动市场上的实地实验的研究,提供了实证证据支持禀赋效应在工资谈判和劳动力市场中的存在。

3."Loss Aversion in Riskless Choice: A Reference-DependentModel"•作者:David E. Bell和Howard Raiffa•这篇论文对禀赋效应和损失厌恶进行了深入的理论分析,建立了一个与参照依赖相关的模型,解释了人们在风险决策中表现出的不对称性。

4."The Endowment Effect: Evidence of Losses Valued Morethan Gains"•作者:Richard H. Thaler•这是一项关于禀赋效应的经典实证研究,提供了证据表明,人们对于拥有的东西的价值往往高于他们愿意为相同物品支付的价格。

5."The Endowment Effect and Repeated Market Trials: Is theVickrey Auction Demand Revealing?"•作者:Charles R. Plott和Kathryn Zeiler•该研究通过重复市场试验,探讨了禀赋效应在拍卖市场中的表现,并对Vickrey拍卖的需求透明性提出了一些观点。

简述基数效用的主要观点

简述基数效用的主要观点

基数效用的主要观点1. 概述基数效用理论是由谢尔登·杜伯来创立的一种心理经济学理论。

该理论认为,人们在做决策时,并不是根据实际效用的大小来选择,而是根据所得到的结果与一个参照点相比较。

基数效用理论主要关注于人们如何对待收益、损失和风险,并提出了一种新的解释方式。

杜伯来认为,人们对待收益和损失的方式是不同的。

当面临盈利情况时,人们倾向于追求安全,而当面临损失时,人们倾向于追求风险。

此外,基数效用理论还提出了风险规避和风险偏好的概念,说明了人们在面临不同的风险时的不同反应。

2. 主要观点2.1 参照点理论参照点理论是基数效用理论的核心概念之一。

参照点是指个体选择行动的基准点。

基数效用理论认为,人们对待收益和损失的方式与参照点的关系密切相关。

当个体的结果超过参照点时,感觉到的满足感较低;而当个体的结果低于参照点时,感觉到的失望感较大。

这种对待收益和损失的方式称为基数效用。

2.2 风险规避和风险偏好基数效用理论提出了风险规避和风险偏好的概念。

根据基数效用理论,人们对待收益和损失的方式是不对等的。

具体来说,人们对待损失更加敏感,更倾向于追求安全。

这就是风险规避的概念。

然而,在面对盈利情况时,人们却更倾向于追求风险,这就是风险偏好的概念。

2.3 无法逆转的决策基数效用理论认为,人们对待盈利和损失的敏感度是不一样的,这导致了人们在做决策时有时会犯下错误,尤其是当损失已经发生时。

基数效用理论称之为“锚定效应”,即人们过度依赖参照点,并无法充分考虑新的信息和更好的选择。

2.4 预期效用和体验效用基数效用理论进一步提出了预期效用和体验效用的概念。

预期效用是指人们在做决策前对结果的主观估值,而体验效用是指人们在实际经历结果后的主观感受。

基数效用理论认为这两种效用是相互独立的,人们在决策时会根据预期效用做出选择,但实际体验结果可能会和预期效用有所偏差。

3. 总结基数效用理论提供了一种新的解释方式来理解人们的决策行为。

心理学中的过度自信与企业管理者的过度自信现象

心理学中的过度自信与企业管理者的过度自信现象

心理学中的过度自信与企业管理者的过度自信现象摘要:近年来,行为金融学兴起并不断发展,其研究的最重要的心理偏差即是过度自信。

本文介绍过度自信现象的心理学解释以及企业管理者过度自信的实证研究例证,并对过度自信现象的研究做出了一些评价。

正文:过度自信是心理学的一个专业术语,是指人们倾向于高估自己成功的概率,而低估失败的概率的心理偏差(Wolosin,et al,1973;Langer,1975)。

Kahneman,Daniel和Amos Tversky(1979)等心理学家通过实证研究发现,人们在形成自己的判断时经常对自己的判断过于自信,高估自己成功的机会,我们把这种心理现象称为过度自信(Overconfidence)。

一、产生过度自信的原因:1、证实性偏见(Confirmation Bias)当我们在主观上支持某种观点的时候,我们往往倾向于寻找那些能够支持我们原来的观点的信息,而对于那些可能推翻我们原来的观点的信息往往忽视掉。

比如,我们讨厌某个国家,那么,我们就会下意识的关注这个国家的负面消息,用以证明这个国家确实不招人喜欢,而且越来越讨厌;在工作中,如果我们赞同某个方案(特别是那些自己提出的方案),也会举出众多理由,数据的、图片的、事实的、分析的,来不断支持该方案,使其越来越正确。

2、难度效应(hard-easy effect)许多研究表明, 人们判断或决策的信心水平受任务难度及领域的影响(Gigerenzer et al, 1991;Kvidera, 2008)。

通常对较难任务做信心水平评估时, 才会引起过分自信和较差的校准。

而任务难度过于简单, 过分自信的现象就会消失;相反,会出现系统的信心不足(Juslin, Winman & Olsson,2000)。

Lichtensten 将这种现象称为信心的难易效应 (Craig et al, 2008)。

人们在面对更难解决的问题时更易产生过度自信。

行为金融学课后答案1至5章anawer

行为金融学课后答案1至5章anawer

第一章1. Differentiate the following terms/concepts:a.Prospect and probability distributionA prospect is a lottery or series of wealth outcomes, each of which is associated with a probability, whereas a probability distribution defines the likelihood of possible outcomes.b.Risk and uncertaintyRisk is measurable using probability, but uncertainty is not. Uncertainty is when probabilities can’t be assigned or the possible outcomes are unclear.c.Utility function and expected utilityA utility function, denoted as u( ), assigns numbers to possible outcomes so that preferred choices receive higher numbers. Utility can be thought of as the satisfaction received from a particular outcome.d.Risk aversion, risk seeking, and risk neutralityRisk aversion describes someone who prefers the expected value of a lottery to the lottery itself. Risk seeking describes someone who prefers a lottery to the expected value of a lottery. And risk neutrality describes someone whose utility of the expected value of a lottery is equal to the expected utility of the lottery.2. When eating out, Rory prefers spaghetti over a hamburger. Last night she had a choice of spaghetti and macaroni and cheese and decided on the spaghetti again. The night before, Rory had a choice between spaghetti, pizza, and a hamburger and this time she had pizza. Then, today she chose macaroni and cheese over a hamburger. Does her selection today indicate that Rory’s choices are consistent with economic rationality? Why or why not?Rory’s pref erences are consistent with rationality. They are complete and transitive. We see that her preference ordering is:Pizza spaghetti macaroni and cheese hamburger3. Consider a person with the following utility function over wealth: u(w) = e w, where e is the exponential function (approximately equal to 2.7183) and w = wealth in hundreds of thousands of dollars. Suppose that this person has a 40% chance of wealth of $50,000 and a 60% chance of wealth of $1,000,000 as summarized by P(0.40, $50,000, $1,000,000).a. What is the expected value of wealth?E(w) = .4 * .5 + .6 * 10 = 6.2U(P) = .4e0.50 + .6e10 = 13,216.54b. Construct a graph of this utility function.The function is convex.c. Is this person risk averse, risk neutral, or a risk seeker?Risk seeker because graph is convex.d. What is this person’s certainty equivalent for the prospect?e w = 13,216.54 gives w = 9.4892244 or $948,922.444. An individual has the following utility function: u(w) = w.5 where w = wealth.a. Using expected utility, order the following prospects in terms of preference, from the most to the least preferred:P1(.8, 1,000, 600)P2(.7, 1,200, 600)P3(.5, 2,000, 300)Ranking: P2, P3, P1 with expected utilities 31.5972, 31.0209, and 30.1972 for prospects 2, 3, and1, respectivelyb. What is the certainty equivalent for prospect P2?998.3830c. Without doing any calculations, would the certainty equivalent for prospect P1 be larger or smaller? Why?The certainty equivalent for P1 would be smaller because P2 is ranked higher than P1.5. Consider two prospects:Problem 1: Choose betweenProspect A: $2,500 with probability .33,$2,400 with probability .66,Zero with probability .01.And Prospect B: $2,400 with certainty.Problem 2: Choose betweenProspect C: $2,500 with probability .33,Zero with probability .67.And Prospect D: $2,400 with probability .34,Zero with probability .66.It has been shown by Daniel Ka hneman and Amos Tversky (1979, “Prospect theory: An analysis of decision under risk,” Econometrica 47(2), 263-291) that more people choose B when presented with problem 1 and when presented with problem 2, most people choose C. These choices violate expected utility theory. Why?This is an example of the Allais paradox. The first choice suggests thatu(2,400) > .33u(2,500) + .66u(2,400) or .34u(2,400) > .33 u(2,500)while the second choice suggests just the opposite inequality.第二章1. Differentiate the following terms/concepts:a. Systematic and nonsystematic riskNondiversifiable or systematic risk is risk that is common to all risky assets in the system and cannot be diversified. Diversifiable or unsystematic risk is specific to the asset in question and can be diversified.b. Beta and standard deviationBeta is the CAPM’s measure of risk. It takes into account an asset’s sensitivity to the market and only measures systematic, nondiversifiable risk. The standard deviation is a measure of dispersion that includes both diversifiable and nondiversifiable risks.c. Direct and indirect agency costsAgency costs arise when managers’ incentives are not consistent with maximizing the value of the firm. Direct costs include expenditures that benefit the manager but not the firm, such as purchasing a luxury jet for travel. Other direct costs result from the need to monitor managers, including the cost of hiring outside auditors. Indirect costs are more difficult to measure and result from lost opportunities.d. Weak, semi-strong, and strong form market efficiencyWith weak form market efficiency prices reflect all the information contained in historical returns. With semi-strong form market efficiency prices reflect all publicly available information. With strong form market efficiency prices reflect information that is not publicly available, such as insiders’ information.2. A stock has a beta of 1.2 and the standard deviation of its returns is 25%. The market risk premium is 5% and the risk-free rate is 4%.a. What is the expected return for the stock?E(R) = .04 + 1.2(.05) = .10b. What are the expected return and standard deviation for a portfolio that is equally invested in the stock and the risk-free asset?E(R p) = .5(.10) +.5(.04) = .07, σp =(.5)(.25) = .125c. A financial analyst forecasts a return of 12% for the stock. Would you buy it? Why or why not?If you believe the source is very credible, buy it as it is expected to generate a positive abnormal (or excess) return.3. What is the joint hypothesis problem? Why is it important?If when testing one hypothesis another must be assumed to hold, a joint-hypothesis problem arises. For us, this is of particular interest when we are testing market efficiency because of the need to utilize a particular risk-adjustment model to produce required returns, that is, to risk-adjust.This would not be a problem if we knew with certainty what the correct risk adjustment model is, but unfortunately we do not. If a test rejects the EMH, is it because the EMH does not hold, or because we did not properly measure abnormal returns? We simply do not know for certain the answer to this question.4. Warren Buffett has been a very successful investor. In 2008 Luisa Kroll reported that Buffett topped Forbes Magazine’s list of the world’s richest people with a fortune estimated to be worth $62 billion (March 5, 2008, "The world's billionaires," Forbes). Does this invalidate the EMH?Warren Buffett’s experience does not necessarily invalidate the EMH. There is the possibility that he is just lucky: given that there are numerous money managers, some are bound to perform well just by luck. Still many would question this here because Buffett’s track record has been consistently strong.5. You are considering whether to invest in two stocks, Stock A and Stock B. Stock A has a beta of 1.15 and the standard deviation of its returns has been estimated to be 0.28. For Stock B, the beta is 0.84 and standard deviation is 0.48.a.Which stock is riskier?Stock A is riskier, though stock B has greater total risk.b.If the risk-free rate is 4% and the market risk premium is 8%, what is the expectedreturn for a portfolio that is composed of 60% A and 40% B?R p = .6(.132) + .4 (.1072) = .12208c.If the correlation between the returns of A and B is 0.50, what is the standarddeviation for the portfolio that includes 60% A and 40% B?σp2 = (.6)2(.28)2 + (.4)2(.48)2+ 2*.5(.6)(.4)(.28)(.48) = 9.7%, σp = 31.2%第三章1. Differentiate the following terms/concepts:a. Lottery and insuranceA lottery is a prospect with a low probability of a high payoff. Many people buy lottery tickets, even with negative expected values. These same people buy insurance to protect themselves from risk. Normally, insurance is a hedge against a low-probability large loss. These choices are inconsistent with traditional expected utility framework but can be explained by prospect theory.b. Segregation and integrationIntegration occurs when positions are lumped together, while segregation occurs when situations are viewed one at a time.c. Risk aversion and loss aversionA person who is risk averse prefers the expected value of a prospect to the prospect itself, whereas for a person who is loss averse, losses loom larger than gains.d. Weighting function and event probabilityEvent probability is simply the subjective view on how likely an event is. The weighting function is associated with the probability of an outcome, but is not strictly the same as the probability as in expected utility theory.2. According to prospect theory, which is preferred?a. Prospect A or B?Decision (i). Choose between:A(0.80, $50, $0)and B(0.40, $100, $0)Prospect A is preferred due to risk aversion for gains. While both have the same expected change in wealth, A has less risk.b. Prospect C or D?Decision (ii). Choose between:C(0.00002, $500,000, $0) and D(0.00001, $1,000,000, $0)Prospect D, with more risk, is preferred due to the risk seeking that occurs when there are very low probabilities of positive payoffs.c. Are these choices consistent with expected utility theory? Why or why not?Violation of EU theory because preferences are inconsistent. The same sort of Allais paradox proof from chapter 1 can be used. It is also necessary to make the assumption of preference homogeneity, which means that if D is preferred to C, it will also be true that D* is preferred to C* where these are:C*:(0.00002, $50, $0) and D*: (0.00001, $100, $0)3. Consider a person with the following value function under prospect theory:v(w) = w.5when w > 0= -2(-w) .5when w < 0a. Is this individual loss-averse? Explain.This person is loss averse. Losses are felt twice as much as gains of equal magnitude.b. Assume that this individual weights values by probabilities, instead of using a prospect theory weighting function. Which of the following prospects would be preferred?P1(.8, 1000, -800)P2(.7, 1200, -600)P3(.5, 2000, -1000)We calculate the value of each prospect:V(P1) = .8(31.62)+.2(-2)(28.27)= 13.982V(P2) = .7(34.64)+.3(-2)(24.49)= 9.55V(P3) = .5(44.72)+.5(-2)(31.62)= 9.265Therefore prospect P1 is preferred.4. Now consider a person with the following value function under prospect theory:v(z) = z.8when z ≥ 0= -3(-z).8when z < 0This individual has the following weighting function:where we set =.65.a. Which of the following prospects would he choose?PA(.001, -5000)PB(-5)Compare the value of each prospect:V(P A) = .983(0) + (-3)(910.28)(.011) = -30.15 (note use of weights)V(PB) = 3 * 1 * -3.62 = -10.87Therefore you would prefer B.b. Repeat the calculation but using probabilities instead of weights. Whatdoes this illustrate?V(P A) = .999 * 0 + 3 * .001 * -910.28 = -2.73 (note use of probability)V(PB) = 3 * 1 * -3.62 = -10.87Therefore you would prefer A. The reason for the switch is that risk seeking is maintained in the domain of losses (implying rejection of losses) if probabilities are used instead of weights.5. Why might some prefer a prix fixe (fixed price) dinner costing about the same as an a la carte one (where you pay individually for each item)? (Assume the food is identical.)Payment decoupling is encouraged with prix fixe. You only face the loss of money once rather than multiple times (occurring if you have to face the cost of each item individually using an à la carte scheme).第五章1. Differentiate the following terms/concepts:a.Primacy and recency effectsA primacy effect is the tendency to rely on information that comes first when making an assessment, whereas a recency effect is the tendency to rely on the most recent information when making an assessment.b.Salience and availabilityThe salience of an event refers to how much it stands out relative to other events, whereas the availability refers to how easily the event is recalled from memory.c.Fast-and-frugal heuristics and bias-generating heuristicsFast and frugal heuristics require a minimum of time, knowledge and computation in order to make choices. Often they lead to very good choices. Sometimes however heuristics go astray and generate behavioral bias.d.Autonomic and cognitive heuristicsAutonomic heuristics are reflexive, autonomic, non-cognitive, and require low effort levels. Cognitive heuristics require more deliberation. Autonomic heuristics are appropriate when a very quick decision must be made or when the stakes are low, whereas cognitive heuristics are appropriate when the stakes are higher.2. Which description of Mary has higher probability?a. Mary loves to play tennis.b. Mary loves to play tennis and, during the summer, averages at least a game aweek.Explain your answer. Define the conjunction fallacy. How does it apply here?Assume for the purpose of illustration that the probability that someone loves to play tennis is .2; the probability that someone plays tennis once or more a week during the summer is .1; and the probability of one or the other of these things is .22.Pr(loves tennis) = .2Pr(loves tennis AND averages 1+)= Pr(loves tennis) + Pr(averages 1+) - Pr(loves tennis OR averages 1+)= .2 + .1 - .22 = .08The second probability has to be less because it has one more requirement (not only do you have to love tennis but you also have to play regularly, but some tennis lovers might just be too busy to do this). When people commit the conjunction fallacy (the belief that the joint probability is more likely than one of its components), they will think the second (joint) event is more likely because it sounds logical that someone who loves tennis will also play regularly.3. Rex is a smart fellow. He gets an A in a course 80% of the time. Still helikes his leisure, only studying for the final exam in half of the courses he takes.Nevertheless when he does study, he is almost sure (95% likely) to get an A.Assuming he got an A, how likely is it he studied? If someone estimates the above to be 75%, what error are they committing? Explain.P(studied|A) = P(A|studied) * [P(studied)/P(A)]= .95 * (.5 / .8) = .59375The “sample” is that he got an A. Without knowing this you would have said the probability that he studied was .5. You rightfully shifted the probability upwards based on the sample, but you moved it too much. You should have stayed closer to the base rate, so you have committed base weight underweighting.Another example of this is, when watching sports and noticing that someone is playing better than they normally do, believing that they have permanently improved.4. Why are two people who witnessed the same event last month likely to describeit differently today?Memory is very imprecise. The common view that past experiences have somehow been writtento the brain’s hard-drive and are then retrieved, even if at considerable effort, is not the way our brain works. In fact, memory is reconstructive. Therefore people in remembering some event will reconstruct it in different ways.5. How do gambling fallacy and clustering illusion relate to representativeness?Provide examples from sports. In what way are they different? Representativeness exists when one thinks that A should look like B. A can be the sample and B the distribution, or vice-versa. A belief in a hot hand is thinking the conditional distribution should look like the sample. But sometimes it seems that people think the reverse, namely that the sample, however small, should look like the distribution, in the sense that essential features should be shared. A hot hand often comes into play in sports when people don’t know for certain the skill level of an athlete, and the extent to which it may change. Gambler’s fallacy is likely to exist when the underlying distribution (e.g., cards or dice) is well-known.。

文献选读-Prospect Theory An Analysis of Decision Under Risk

文献选读-Prospect Theory An Analysis of Decision Under Risk
Reference Study Report
Prospect Theory: An Analysis of Decision Under Risk
Teacher: Prof. Yuanlue Fu Student: Liang Lizhen
Reference Study Report
Prospect Theory: An Analysis of Decision Under Risk
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Reference Study Report
Tenets of expected utility theory
Expectation: U(x1,p1;…;xn,pn)=p1u(x1)+…+pnu(xn). -Implying the independence axiom
Discussion
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Reference Study Report
Some Definitions
A prospect (x1,p1;…;xn,pn) is a contract that yields outcome xi with probability pi, where p1+p2+…+pn=1.
Violation of Expected Utility Theory
— The Reflection Effect
Preferences Between Positive and Negative Prospects
Positive prospects
Negative prospects
Problem3: (4000, .80)<(3000)
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Although the domain of the utility function is not limited to any particular class of consequences, most applications of the theory have been concerned with monetary outcomes. Furthermore, most economic applications introduce the following additional assumption.
1This work was supported in part by grants from the Harry F. Guggenheim Foundation and from the Advanced Research Projects Agency of the Department of Defense and was monitored by Office of Naval Research under Contract N00014-78-C-0100 (ARPA Order No. 3469) under Subcontract 78-072-0722 from Decisions and Designs, Inc. to Perceptronics, Inc. We also thank the Center for Advanced Study in the Behavioral Sciences at Stanford for its support.
MARCH, 1979
NUMBER 2
PROSPECT THEORY: AN ANALYSIS OF DECISION UNDER RISK
BY DANIELKAHNEMANANDAMOSTVERSKY'
This paper presents a critique of expected utility theory as a descriptive model of decision making under risk, and develops an alternative model, called prospect theory. Choices among risky prospects exhibit several pervasive effects that are inconsistent with the basic tenets of utility theory. In particular, people underweight outcomes that are merely probable in comparison with outcomes that are obtained with certainty. This tendency, called the certainty effect, contributes to risk aversion in choices involving sure gains and to risk seeking in choices involving sure losses. In addition, people generally discard components that are shared by all prospects under consideration. This tendency, called the isolation effect, leads to inconsistent preferences when the same choice is presented in different forms. An alternative theory of choice is developed, in which value is assigned to gains and losses rather than to final assets and in which probabilities are replaced by decision weights. The value function is normally concave for gains, commonly convex for losses, and is generally steeper for losses than for gains. Decision weights are generally lower than the corresponding probabilities, except in the range of low probabilities. Overweighting of low probabilities may contribute to the attractiveness of both insurance and gambling.
The application of expected utility theory to choices between prospects is based on the following three tenets.
(i) Expectation: U(X1, Pi; ... ; Xn,Pn)= pi u (x1) +... +PnU (Xn)
Prospect Theory: An Analysis of Decision under Risk Author(s): Daniel Kahneman and Amos Tversky Source: Econometrica, Vol. 47, No. 2 (Mar., 1979), pp. 263-292 Published by: The Econometric Society Stable URL: /stable/1914185 . Accessed: 13/09/2011 10:51 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . /page/info/about/policies/terms.jsp JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@.
263
264
D. KAHNEMAN AND A. TVERSKY
That is, the overall utility of a prospect, denoted by U, is the expected utility of its outcomes.
(ii) Asset Integration: (xi, Pi; ... ; Xn,P) is acceptable at asset position w iff U(w +x1, pl; ... ; w +Xn,Pn)> u(w).
That is, a prospect is acceptable if the utility resulting from integrating the prospect with one's assets exceeds the utility of those assets alone. Thus, the domain of the utility function is final states (which include one's asset position) rather than gains or losses.
2. CRITIQUE
Decision making under risk can be viewed as a choice between prospects or gambles. A prospect (x1, Pi; ... ; xn,pn)is a contract that yields outcome xi with probability Pi, where Pl + P2 + ... + pn = 1. To simplify notation, we omit null outcomes and use (x, p) to denote the prospect (x, p; 0, 1- p) that yields x with probability p and 0 with probability 1-p. The (riskless) prospect that yields x with certainty is denoted by (x). The present discussion is restricted to prospects with so-called objective or standard probabilities.
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