Showing papers on "Von Neumann–Morgenstern utility theorem published in 1993"
TL;DR: In this paper, the authors present a method for axiomatizing a variety of models for decision making under uncertainty, including Expected Utility and Cumulative Prospect Theory, and identify situations that permit consistent inferences about the ordering of value differences.
Abstract: This paper presents a method for axiomatizing a variety of models for decision making under uncertainty, including Expected Utility and Cumulative Prospect Theory. This method identifies, for each model, the situations that permit consistent inferences about the ordering of value differences. Examples of rankdependent and sign-dependent preference patterns are used to motivate the models and the “tradeoff consistency” axioms that characterize them. 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.
480 citations
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TL;DR: It is shown that if the authors define risk and value in appropriate ways, the rank order produced by the risk-value model will be consistent with a suitably chosen expected utility or non-expected utility model.
229 citations
TL;DR: In this paper, a tiny utility of gambling is added to an expected utility model for a risk-averse individual to explain small payoff gambles, large prize lotteries, and patterns of risk-seeking in the experimental evidence that are puzzling from the viewpoint of standard theory.
Abstract: A tiny utility of gambling is appended to an expected utility model for a risk-averse individual. It is shown that the model can explain small payoff gambles, large prize lotteries, and patterns of risk-seeking in the experimental evidence that are puzzling from the viewpoint of standard theory. At the same time, the model maintains expected utility theory's ability to explain insurance purchase, portfolio diversification, and other risk-averting behavior. The tiny utility of gambling could equally well be appended to models of risky choice other than the expected utility model.
168 citations
TL;DR: In this article, the implications of weak Pareto-weak pareto for Harsanyi's Social Aggregation Theorem are investigated. But they are restricted to the case where the preferences are assumed to satisfy the expected utility hypothesis and are represented by von Neumann-Morgenstern utility functions.
Abstract: Harsanyi's Social Aggregation Theorem is concerned with the aggregation of individual preferences defined on the set of lotteries generated from a finite set of basic prospects into a social preference. These preferences are assumed to satisfy the expected utility hypothesis and are represented by von Neumann-Morgenstern utility functions. Harsanyi's Theorem says that if Pareto Indifference is satisfied, then the social utility function must be an affine combination of the individual utility functions. This article considers the implications for Harsanyi's Theorem of replacing Pareto Indifference with Weak Pareto.
58 citations
TL;DR: In two experiments as mentioned in this paper, the authors analyzed Fanning-out patterns of responses to hypothetical lottery choice questions within a Marschak-Machina triangle and found that a large proportion of the observed patterns in the on-border treatment support Hypothesis II, with a considerable amount of fanningout behavior observed.
Abstract: In two experiments we test Machina's Hypothesis II (fanning-out). In each experiment we analyze patterns of responses to hypothetical lottery choice questions within a Marschak-Machina triangle. One set of questions involves lotteries on the border of the triangle, an the other set of questions involves lotteries in the interior of the triangle (off the border). Our results show that a large proportion of the observed patterns in the on-border treatment support Hypothesis II, with a considerable amount of fanning-out behavior observed. The patterns observed in the off-border treatment are significantly different from those in the on-border treatment. Hypothesis II performs well in the off-border treatment because expected utility theory itself, which satisfies the restrictions of Hypothesis II, performs well.
56 citations
TL;DR: A review of the early axiomatic treatments of quasi-linear means developed in the late 1920s and the 1930s can be found in this paper, where the Na- gumo-Kolmogorov theorem and de Finetti's extension of it are discussed.
Abstract: This paper reviews the early axiomatic treatments of quasi- linear means developed in the late 1920s and the 1930s. These years mark the beginning of both axiomatic and subjectivist probability theory as we know them today. At the same time, Kolmogorov, de Finetti and, in a sense, Ramsey took part in a perhaps lesser known debate concerning the notions of mean and certainty equivalent. The results they developed offer interesting perspectives on computing data summaries. They also anticipate key ideas in current normative theories of rational decision making. This paper includes an extended and self-contained introduction dis- cussing the main concepts in an informal way. The remainder focusses primarily on two early characterizations of quasi-linear means: the Na- gumo-Kolmogorov theorem and de Finetti's extension of it. These results are then related to Ramsey's expected utility theory, to von Neumann and Morgenstern's and to results on weighted means.
43 citations
TL;DR: In this paper, the dependence of the decision maker's preferences over consequences on the states of nature is represented by state-specific mappings of the set of consequences onto itself, and it is shown that there exist subjective expected utility representations of the preference relation over acts with unique, nonatomic, probability measure on the algebra of all events.
39 citations
TL;DR: Theorem 3.1 in this article requires the value function to be well-defined and the consumption space to be bounded, which is not suitably defined in [1], especially when a unbounded consumption set is assumed.
Abstract: The paper by C. Ma [1] contains several errors. First, statement and proof of Theorem 2.1 on the existence of intertemporal recursive utility function as a unique solution to the Koopmans equation must be amended. Several additional technical conditions concerning the consumption domain, measurability of certainty equivalent and utility process need to be assumed for the validity of the theorem. Second, the assumptions for Theorem 3.1 need to be amended to include the Feller's condition that, for any bounded continuous functionf e C(S × ℛn
+), μ(f(St+1, θ)¦st =s) is bounded and continuous in (s, θ). In addition, for Theorem 3.1, the pricep, the endowmente and the dividend rateδ as functions of the state variables e S are assumed to be continuous. The Feller's condition for Theorem 3.1 is to ensure the value function to be well-defined. This condition needs to be assumed even for the expected additive utility functions (See Lucas [2]). It is noticed that, under this condition, the right hand side of equation (3.5) in [1] defines a bounded continuous function ins andφ. The proof of Theorem 3.1 remains valid with this remark in place. A correct version of Theorem 2.1 in [1] is stated and proved in this corrigendum. Ozaki and Streufert [3] is the first to cast doubt on the validity of this theorem. They point out correctly that additional conditions to ensure the measurability of the utility process need to be assumed. This condition is identified as conditionCE
4 below. In addition, I notice that, the consumption space is not suitably defined in [1], especially when a unbounded consumption set is assumed. In contrast to what claimed in [3], I show that the uniformly bounded consumption setX and stationary information structure are not necessary for the validity of Theorem 2.1.
29 citations
TL;DR: In this paper, the authors apply Segal's result to prove that Theorem 2 is still valid with minor modifications, and show that the central unifying proposition of expected utility theory is still true.
21 citations
AT&T1
TL;DR: In this article, the effects of the independence axioms on subset utilities include several additive and multiplicative decompositions, as well as skew symmetric bilinear utility theory.
20 citations
TL;DR: In this article, the authors extend the existing literature concerning the relationship between two parameter decision models and those based on expected utility in two main directions, and show that a two-parameter representation of preferences over uncertain prospects and the expected utility representation yield consistent rankings of random variables when the decision maker's choice set is restricted to random variables differing by mean shifts and monotone mean-preserving spreads.
Abstract: This paper extends the existing literature concerning the relationship between two parameter decision models and those based on expected utility in two main directions. The first relaxes Meyer's location and scale (or Sinn's linear class) condition and shows that a two-parameter representation of preferences over uncertain prospects and the expected utility representation yield consistent rankings of random variables when the decision maker's choice set is restricted to random variables differing by mean shifts and monotone meanpreserving spreads. The second shows that the rank-dependent expected utility model is also consistent with two-parameter ranking methods if the probability transform satisfies certain dominance conditions. The main implication of these results is that the simple two-parameter model can be used to analyze the comparative statics properties of a wide variety of economic models, including those with multiple sources of uncertainty when the random variables are comonotonic. To illustrate this point, we apply our results to the problem of optimal portfolio investment with random initial wealth. We find that it is relatively easy to obtain strong global comparative statics results even if preferences do not satisfy the independence axiom.
TL;DR: In this paper, the authors generalize the Nash bargaining solution to the case where decision makers are not necessarily expected utility maximizers, and show that the two extensions coincide when the preferences are of the EU and the rank dependent utility (RDU) types.
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TL;DR: In this article, the authors consider the extent to which individual choice behavior can be controlled, in the manner predicted by expected utility theory, by experimental designs which employ binary lottery payoffs.
Abstract: Considerable evidence has accumulated which shows that the choice behavior of individuals exhibits systematic departures from expected utility maximization. The focus of the paper is to develop some measures of the extent to which utility maximization nevertheless remains a useful approximation. We do this by considering the extent to which individual choice behavior can be controlled, in the manner predicted by expected utility theory, by experimental designs which employ binary lottery payoffs in the manner of Roth and Malouf (1979) and Berg et al. (1986). The results of this study suggest that the gross features of risk preference can be reliably implemented, albeit with a non-negligible amount of error. Some errors were found to be systematic and can be attributed to subjects who did not know how to calculate the expected probbility of winning the prize in a compound binary lottery. The knowledge of compound lotteries also played the role in determinint which funcitonal forms are easier to induce.
TL;DR: In this article, the authors deal with nonexpected utility preferences over multivariate distributions and present two equivalent dominance axioms, implying an additively separable structure of the local utility functions.
Abstract: This paper deals with nonexpected utility preferences over multivariate distributions. We present two equivalent dominance axioms, implying an additively separable structure of the local utility functions. They also imply that nonexpected utility functionals directly depend on the marginals of the multivariate distributions. We define an invariance axiom, show that it is equivalent to the property that all local utility functions are ordinally equivalent, and that it implies an additively separable expected utility functional when the dominance axiom is assumed. An interesting property of multivariate preferences is that risk neutrality does not imply affinity of the utility function over nonstochastic outcomes.
TL;DR: In this article, the envelope theorem is applied to the indirect expected utility function to derive estimating equations for risky assets without making a priori assumptions about the form of the utility function.
Abstract: This article obtains demand functions for risky assets without making a priori assumptions about the form of the utility function. In a simple portfolio model, the envelope theorem is applied to the indirect expected utility function to derive estimating equations. Tests for the existence of constant absolute or constant relative risk aversion are also developed. Empirical estimation of the demand for financial assets held by U.S. households for the period 1946–1985 indicates that aggregate household behavior is consistent with the existence of constant relative risk aversion, with the coefficient of risk aversion having a value of approximately 1.3.
TL;DR: In this paper, it was shown that the effect of an increase in risk on the level of saving depends only on the elasticity of intertemporal substitution and not on the risk aversion parameter.
Abstract: There has been an extensive discussion of optimal consumption-saving behavior of expected utility maximizing risk averse individuals [6; 7]. There are, however, two limitations of such works. First, the widely used time additive von Neumann Morgenstern (VNM) preferences may not be suitable for analyzing choice problems in a dynamic context. Since for this class of preferences the coefficient of relative risk aversion turns out to be the reciprocal of the elasticity of intertemporal substitution, these preferences fail to distinguish between the importance of intertemporal substitution and risk aversion in determining the optimal choice for the individual decision maker. Secondly, in analyzing the comparative static effect of an increase in risk, the increase in risk has been usually captured by the mean preserving spread of the distribution of the underlying random variable. But, since the mean of the distribution is stipulated to be unchanged, the mean preserving spread, undoubtedly, provides a restrictive characterization of an increase in risk. The limitation of the VNM preferences has motivated researchers to look for an alternative framework to analyze dynamic choices under uncertainty. It was Selden [8; 9] who developed a nonexpected utility maximizing approach by proposing the Ordinal Certainty Equivalent (OCE) preferences to distinguish between intertemporal substitution and risk aversion. Since then a number of other authors have further examined the implications of the nonexpected utility maximizing framework. Not surprisingly, in the literature of nonexpected utility maximizing analysis a considerable attention has been given to the individual saving decision under capital risk. In a clear departure from the expected utility maximizing analysis, under the nonexpected utility maximizing approach, optimal saving tends to be determined by the elasticity of intertemporal substitution as well as the risk aversion parameter. However, even in the nonexpected utility maximizing framework, the increase in capital risk has usually been characterized in terms of a mean preserving spread of the random rate of return. It has been shown by Selden [9] and Weil [10] that the effect of an increase in capital risk on the level of saving depends only on the elasticity of intertemporal substitution and not on the risk
TL;DR: In this article, the authors describe two models of asset markets and portfolio choice: one where the von Neumann-Morgenstern utility function is defined on the non-negative real line and short-selling is not allowed, and another where the Von Neumann Morgen Stern utility functions are defined over the entire real line, and short selling may be possible.
TL;DR: In this article, a simple principle, expressible by a single equation, runs through intertemporal consumer behavior: the effect of any given variations of consumption on the utility must be balanced against the impact of such variations on subsequent stocks of assets.
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TL;DR: In this article, the authors suggest that standard expected utility is violated in a wide variety of ways: losses are treated differently from gains, people are generally risk averse over gains and risk loving over losses, fanning and curvature effects exist, problem representation matters, and preference reversals are pervasive.
Abstract: Recent experimental evidence suggests that standard expected utility is violated in a wide variety of ways: losses are treated differently from gains, people are generally risk averse over gains and risk loving over losses, fanning and curvature effects exist, problem representation matters, and preference reversals are pervasive An effort is made to suggest how these effects will change results from models based on expected utility theory, and how researchers who use expected utility in their analysis should react to these findings
TL;DR: In this article, the authors distinguish between risk aversion and intertemporal substitution, and provide an explanation about the observed discrepancy in the empirical estimates of the risk aversion coefficient in the Epstein-Zin nonexpected utility.
Abstract: If asset returns are i.i.d. over time, the preference parameter in the time additive von Neumann-Morgenstern expected utility is the risk aversion coefficient in the Epstein-Zin nonexpected utility. By distinguishing between risk aversion and intertemporal substitution, this article provides an explanation about the observed discrepancy in the empirical estimates of the risk aversion coefficient.
25 Apr 1993
TL;DR: The author discusses the expected value of including uncertainty in decision making, and also normative bases of ambiguity aversion, and there are broad classes of utility functions for which uncertainty is irrelevant under expected utility theory, and only mean values are significant.
Abstract: The author discusses the expected value of including uncertainty in decision making, and also normative bases of ambiguity aversion. It is shown that there are broad classes of utility functions for which uncertainty is irrelevant under expected utility theory, and only mean values are significant. Conversely, there are broad classes of utility functions for which preferences over ambiguity are normatively valid. Finally, preferences over ambiguity, even if valid, are not always relevant to decision making; decision makers may have lower expected utility when a probability is ambiguous than when it is certain, but have the same set of optimal decisions in either case. >
TL;DR: In this article, the authors show that the equilibrium price of equity is distinct from that implied by any intertemporally additive expected utility satisfying specified regularity conditions, in that sense the more general utility functions are observationally distinguishable from the standard expected utility specification.
Abstract: In a Lucas (1978) model, with a Kreps-Porteus (1978) nonexpected utility, the following property of equilibrium holds generically in the space of finite-state, Markov output growth rate processes: equilibrium price of equity is distinct from that implied by any intertemporally additive expected utility satisfying specified regularity conditions. In that sense the more general utility functions are observationally distinguishable from the standard expected utility specification.