An axiomatic theory of conjoint, expected risk (original) (raw)

Axiomatic measures of perceived risk: Some tests and extensions

Journal of Behavioral Decision Making, 1989

The history of axiomatic measurement of perceived risk of unidimensional risky choice alternatives is briefly reviewed. Experiments 1 and 2 present data that distinguish between two general classes of risk functions (those that assume that gain and loss components of an alternative combine additively versus multiplicatively) on empirical grounds. The most viable risk model on the basis of these and other results is described. Experiment 3 presents data that call into question the descriptive adequacy of some of this risk model's assumptions, in particular the expectation principle. Suggestions for possible modifications are made.

Decision under Risk: The Classical Expected Utility Model

Decision-making Process, 2009

Ce chapitre d'ouvrage collectif a pour but de présenter les bases de la modélisation de la prise de décision dans un univers risqué. Nous commençons par dé…nir, de manière générale, la notion de risque et d'accroissement du risque et rappelons des dé…nitions et catégorisations (valables en dehors de tout modèle de représentation) de comportements face au risque. Nous exposons ensuite le modèle classique d'espérance d'utilité de von Neumann et Morgenstern et ses principales propriétés. Les problèmes posés par ce modèle sont ensuite discutés et deux modèles généralisant l'espérance d'utilité brièvement présentés. Mots clé: risque, aversion pour le risque, espérance d'utilité, von Neumann et Morgenstern, Paradoxe d'Allais. JEL: D81

Risk attitudes in axiomatic decision theory: a conceptual perspective

Theory and Decision, 2018

In this paper, I examine the decision-theoretic status of risk attitudes. I start by providing evidence showing that the risk attitude concepts do not play a major role in the axiomatic analysis of the classic models of decision-making under risk. This can be interpreted as reflecting the neutrality of these models between the possible risk attitudes. My central claim, however, is that such neutrality needs to be qualified and the axiomatic relevance of risk attitudes needs to be re-evaluated accordingly. Specifically, I highlight the importance of the conditional variation and the strengthening of risk attitudes, and I explain why they establish the axiomatic significance of the risk attitude concepts. I also present several questions for future research regarding the strengthening of risk attitudes.

How information about probabilities and pay-offs is combined in risk judgment?

In this approach, different psychological transformations on payoffs and probabilities are introduced to account for inconsistencies between actual risk rates and the expectation principle (e.g. E.U. Weber, Anderson and Birnbaum, 1992). In general, such models of perceived risk reflect extensions introduced into the models of expected or non-expected utility preferences (which range from expected value and expected/weighted utility to configural weighting and rank dependent utility models).

Alternative Models of Risk Behavior

Risk Analysis in Theory and Practice, 2004

The expected utility model provides the basis for most of the research on the economics of risk. It was the topic presented in Chapter 3. Under the expected utility model, individuals make decisions among alternative wealth levels x by maximizing EU(x) where E is the expectation operator. The utility function U(x) is defined up to a positive linear transformation. It is sometimes called a von Neumann-Morgenstern utility function. We saw in Chapter 4 that risk aversion, risk neutrality, or risk loving preferences correspond to the function U(x) being respectively concave, linear, or convex. One of the main advantages of the expected utility model is its empirical tractability. This is the reason why it is commonly used in risk analysis. But is the expected utility model a good predictor of human behavior? Sometimes, it is. And sometimes, it is not. This chapter evaluates some of the evidence against the expected utility model. It also reviews alternative models that have been proposed to explain behavior under risk. The first challenge to the expected utility model is the following: Is it consistent with the fact that some individuals both insure and gamble at the same time? Friedman and Savage proposed to explain this by arguing that, for most individuals, the utility function U(x) is probably concave (corresponding to risk aversion and a positive willingness to insure) for low or moderate monetary rewards, but convex (corresponding to risk loving and a positive willingness to gamble) for high monetary rewards. In this context, a particular individual can insure against ''downside risk'' while at the same time gambling on ''upside risk'' and still be consistent with the expected utility model.

Models of risk and choice: challenge or danger

A dimensional model of perceived risk and a model of risk acceptance based on risk rates are proposed in this paper. In line with the proposed model of perceived risk, risk is a linear combination of the three basic dimensions of a risky situation: the amount and probability of loss and the amount of gain. It is assumed that psychological transformations are made on these dimensions. According to the model of acceptance, acceptance is judged by making a trade-o between perceived risk and the amount of gain. These models have been investigated in two experiments, in which risk judgments and acceptance rates for a set of descriptions of risky investments were collected from managers in Poland. The proposed dimensional model of perceived risk was compared to the distributional models of risk and to the risk models based on the expectation principle. The best ®t was obtained for the proposed model. It was also found that perceived risk was useful in predicting acceptance rates. Better ®ts were obtained for the models of acceptance, based on perceived risk, than for the expected/weighted utility models, including bilinear models. Ó

Risk, ambiguity, and the separation of utility and beliefs

Mathematics of Operations Research, 2001

We introduce a general model of static choice under uncertainty, arguably the weakest model achieving a separation of cardinal utility and a unique representation of beliefs. Most of the non-expected utility models existing in the literature are special cases of it. Such separation is motivated by the view that tastes are constant, whereas beliefs change with new information. The model has a simple and natural axiomatization.