We present a new theory of decision under uncertainty. Cambridge core microeconomics prospect theory by peter p. This model, cumulative prospect theory cpt, as well as related models proposed by other authors, has received wide acclaim. Empirical estimates indicate that wp is regressive with respect to the diagonal wp p for small p, and wp. Cumulative prospect theory for parametric and multiattribute. Prospect theory involves two phases in the decision making process. We develop a new version of prospect theory that employs cumulative rather than separable decision weights and extends the theory in several respects. An axiomatization of cumulative prospect theory for decision. First, we extract the decision attributes through analyzing the factors affecting shipping safety investment. The major properties of the value function in cumulative prospect theory diminishing sensitivity and loss aversion are contrasted with the principle of diminishing marginal utility that is commonly assumed in expected utility.
The difference between this version and the original version of prospect theory is that weighting is applied to the cumulative probability. When discussing the axiomatization of stochastic models for choices over a set of alternatives, as seen in dagsvik 2008, the nature of probabilistic choice are originally given. Pdf an axiomatization of cumulative prospect theory for. This paper presents a method for axiomatizing a variety of models for decision making under uncertainty, including expected utility and cumulative prospect theory. The model has been imported into a number of fields and has been used to analyze various aspects. In the framing phase, the decision maker constructs a representation of the acts, contingen. Cumulative prospect theory cpt, the leading behavioral account of decision making under uncertainty, assumes that the probability weight applied to a given outcome depends on its ranking. A probability weighting function wp is a prominent feature of several nonexpected utility theories, including prospect theory and rankdependent models. The prospect theory is an economics theory developed by daniel kahneman and amos tversky in 1979. Cumulative prospect theory was introduced by tversky and kahneman so as to combine the empirical realism of their original prospect theory with the theoretical advantages of quiggins rankdependent utility. There is no preference axiomatization of cumulative prospect theory available for risk yet, i. It shows that cumulative prospect theory is not merely a formal correction of some theoretical problems in prospect theory, but it also gives dierent predictions. This note provides a foundation of prospect theory, where referencedependence is derived from preference conditions and a unique reference point arises endogenously.
For example, prospect theory explains a lot of gambling behavior, such as the tendency of people to continue gambling when they have losses. We devise a simple test involving threeoutcome lotteries, based. Variants of cumulative prospect theory are increasingly widely applied in both theoretical and. Cpt is one of the most promising alternatives to expected utility theory since it incorporates loss aversion, and linear utility for.
An axiomatization of linear cumulative prospect theory with applications to portfolio selection and insurance demand by ulrich schmidta and horst zank yeb. Available information and psychological attitude facing ambiguity jointly determine the subjective likelihood. This version, called cumulative prospect theory, applies to uncertain as well as to risky prospects with any number of outcomes, and it allows different weighting functions for gains and for losses. Endogenizing prospect theorys reference point semantic. This retains the predictive power of previous versions of prospect theory, but extends that theory by allowing reference points to be uncertain while decision weights are specified in a rankdependent way. At its heart, social psychology investigates how situationstypically social situationsinfluence judgment and behavior. That is why kahneman was ultimately awarded the nobel prize. Thirdgeneration prospect theory university of nottingham. This paper provides an axiomatization of a new specification of cumulative prospect theory, termed endogenous prospect theory, where referencedependence is derived from preference conditions and a unique reference point arises endogenously. Endogenizing prospect theorys reference point semantic scholar. A revised version, called cumulative prospect theory overcame this problem by using a probability weighting function derived from rankdependent expected utility theory.
It shows that cumulative prospect theory is not merely a formal. Tversky and kahneman 1992 developed a theory called cumulative prospect theory. It is a further development and variant of prospect theory. Prospect theory, psychological theory of decisionmaking under conditions of risk, which was developed by psychologists daniel kahneman and amos tversky and originally published in 1979 in econometrica. In previous models of cumulative prospect theory referencedependence of preferences is imposed beforehand and the location of the reference point is exogenously determined. All those axiomatizations, however, only consider decision under uncertainty. Qualityadjusted lifeyears qalys are the most common utility measure in medical decision analysis and economic evaluations of health care. An axiomatization of cumulative prospect theory for decision under risk. Reference dependence in cumulative prospect theory. Two conclusions can be drawn from the recent literature on decision making under risk.
Prospect theory has had wide ranging implications and applications. A characterization of qualityadjusted lifeyears under. All exosting axiomatizations, however, only consider decision under uncertainty, and no axiomatization has as yet been provided for decision. An axiomatization of linear cumulative prospect theory. Tthis version is the one typically used in economic analysis, and it is the version his version is the one typically used in economic analysis, and it. Pdf cumulative prospect theory was introduced by tversky and kahneman so as to combine the empirical realism of their original prospect. A second central feature of prospect theory and cumulative prospect theory cpt is the fact that the value function depends on gains and losses relative to a reference point or status quo and not on final wealth positions as in expected utility theory. To study the tendency of shipping safety investment decisionmaking with different risk perception and appetite, a decisionmaking method based on cumulative prospect theory is proposed in this article.
A discussion of empirical dierences hein fennema university of nijmegen, the netherlands peter wakker university of leiden, the netherlands abstract this paper discusses dierences between prospect theory and cumulative prospect theory. Some experiments by lola lopes are reanalyzed, and are demonstrated to favor cumulative prospect theory over prospect theory. An analysis of decision under risk by daniel kahneman and amos tversky 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. An axiomatization of cumulative prospect theory 1993. Direct tests of cumulative prospect theory harvard economics. Cumulative prospect theory was introduced by tversky and kahneman so as to combine the empirical realism of their original prospect theory with the theoret. Several axiomatizations of cpt can be found in the literature. Cumulative prospect theory and imprecise risk lirmm. An axiomatization of linear cumulative prospect theory with. Prospect theory pt or its successor cumulative prospect theory, both introduced by kahneman and tversky 17, 18, which we will apply to attempt modelling risky security decisions. Cumulative prospect theory meets reinforcement learning.
This paper presents an axiomatization of cumulative prospect theory, which. Much of the literature only estimates a subset of cpt parameters, or more simply assume cpt parameter values from prior studies. Incorporating cumulative prospect theory into decision analysis can provide a form of sensitivity analysis and may help describe when people deviate from expected utility theory. C u m u lative representation of uncertainty a m o s t v e r s k y stanford u niversity, department o f psychology, stanford, c a 943052 d a n ie l k a h n e m a n u niversity o f california a t berkeley, department o f p sychology, berkeley, c a 94720 key w o rd s. A genuine foundation for prospect theory, journal of risk. An axiomatic analysis of cumulative prospect theory is presented in the appendix.
Tversky and kahneman, 1992 that the basic elements of prospect theory are compatible with the cumulative functional, and that it is possible to construct a model that combines these approaches to produce what we call cumulative prospect theory. Jul 09, 2019 prospect theory assumes that losses and gains are valued differently, and thus individuals make decisions based on perceived gains instead of perceived losses. Pdf an axiomatization of cumulative prospect theory for decision. Box 616, 6200 md maastricht, the netherlands august 17, 1998 abstract in cumulative prospect theory models, di. An axiomatization of cumulative prospect theory semantic scholar. C u m u lative representation of uncertainty a m o s t v e r s k y stanford u niversity, department o f psychology, stanford, c a 943052 d a n ie l k a h n e m a n u niversity o f california a t berkeley, department o f p sychology, berkeley, c a 94720. Secondly, whatever the axiomatization, neither are the relations between the two capacities specified in the cpt model, nor their interpretation clearly founded. This assumption is needed to avoid the violations of dominance implied by prospect theory pt. An axiomatization of cumulative prospect theory for. It shows that cumulative prospect theory is not merely a formal correction. This value function has two parts, a concave part in the gain domain. Prospect theory explains how situational variability in the way a decision is framed can have a dramatic impact on the decisions people make.
According to prospect theory, people are typically riskaverse with respect to gains and riskseeking with respect to losses, known as the reflection effect. A genuine foundation for prospect theory a genuine foundation for prospect theory schmidt, ulrich. In this case, however, reference dependence and the dependence of the value function on final wealth positions are equivalent concepts, at least if the status quo is known. We take cumulative prospect theory cpt seriously by rigorously estimating structural models using the full set of cpt parameters. Accordingly, a value function v replaces the standard utility function. Citeseerx document details isaac councill, lee giles, pradeep teregowda. More precisely, we will use cumulative prospect theory cpt, a later, re. Oct 15, 2014 prospect theory is widely viewed as the best available descriptive model of how people evaluate risk in experimental settings. An axiomatization of cumulative prospect theory 151 sign profile, i. An axiomatization of linear cumulative prospect theory with applications to portfolio selection and insurance demand by ulrich schmidt and horst zank get pdf 281 kb. The pension mode provided by the government alone can no longer meet the social demand, and the governments purchase of homebased care services from social organizations has become a new trend. Examples of rankdependent and signdependent preference patterns are used to motivate the models. Theory prospect theory distinguishes two phases in the choice process.
The present paper combines loss attitudes and linear utility by providing an axiomatic analysis of corresponding preferences in a cumulative prospect theory cpt. Cumulative prospect theory can also be used for infinitely many or even continuous outcomes for example, if the outcome can be any real number. An axiomatization of linear cumulative prospect theory with applications to portfolio selection and insurance demand. Although the theory is meant to apply to both uncertainty and risk, preference axiomatizations have hitherto been provided only for decision under uncertainty. The present paper combines loss attitudes and linear utility by providing an axiomatic analysis of corresponding preferences in a cumulative prospect theory cpt framework. First, cumulative prospect theory cpt is nowadays the most promising alternative to expected utility theory. An axiomatization of cumulative prospect theory springerlink. It suggests that people think of possible outcomes based on a certain point of reference instead of a final status or outcome. Peter wakker medical decision making unit, leiden uni ersity medical center, the netherlands abstract cumulative prospect theory was introduced by tversky and kahneman so as to combine the empirical.
Pdf the probability weighting function semantic scholar. Only when both conditions are met is it ensured that for each state the weight assigned by the decision maker is the same for all prospects. Cumulative prospect theory, or cpt, was introduced in 1992 by amos tversky and daniel kahneman. Cumulative prospect theory and imprecise risk fabrice philippe. The result for risk turns out to be considerably simpler than that for. Preference axiomatizations were provided in several papers. Cumulative prospect theory for parametric and multiattribute utilities horst zank dept. An axiomatization of cumulative prospect theory core. Prospect theory is widely viewed as the best available descriptive model of how people evaluate risk in experimental settings. It was axiomatized differently from rank and signdependent utility theory, and it also made different assumptions about values and decision weights. In order to identify the differences between both concepts, an axiomatization of cumulative prospect theory is developed which allows for a variable status quo. This paper presents an axiomatization of qalys under cumulative prospect theory cpt, currently the most influential model for decision under uncertainty. Axiomatization definition of axiomatization by the free.
Prospect theory distinguishes two phases in the choice process. In the first two lines of the proof of lemma a1 there are eight a2s. Cpt differs from the standard prospect theory by adding weight to the cumulative probability distribution function. Sugdens axiom system implies maximisation of the function.
This paper presents a method for axiomatizing a variety of models for decision making under uncertainty, including expected utility and cumulative prospect. The magnitude of benefit estimated in a decisionanalytic model can change significantly after using cumulative prospect theory. A simple model of cumulative prospect theory by ulrich schmidta and horst zankb. This paper presents principles that provide critical tests and foundations for prospect. Decision analysis with cumulative prospect theory ahmed.
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