Showing papers on "Von Neumann–Morgenstern utility theorem published in 2011"
03 Aug 2011
TL;DR: It is shown that bounded optimal control solutions can be derived from this variational principle, which leads in general to stochastic policies, and that risk-sensitive and robust control schemes fall out naturally if the environment is considered as a bounded rational and perfectly rational opponent, respectively.
Abstract: Perfectly rational decision-makers maximize expected utility, but crucially ignore the resource costs incurred when determining optimal actions Here we employ an axiomatic framework for bounded rational decision-making based on a thermodynamic interpretation of resource costs as information costs This leads to a variational "free utility" principle akin to thermodynamical free energy that trades off utility and information costs We show that bounded optimal control solutions can be derived from this variational principle, which leads in general to stochastic policies Furthermore, we show that risk-sensitive and robust (minimax) control schemes fall out naturally from this framework if the environment is considered as a bounded rational and perfectly rational opponent, respectively When resource costs are ignored, the maximum expected utility principle is recovered
81 citations
TL;DR: It is argued that the one-switch property is a natural generalization of utility independence and shown how it leads to tractable multiattribute utility functions.
Abstract: Assessment of multiattribute utility functions is significantly simplified if it is possible to decompose the function into more manageable pieces. Utility independence is a powerful property that serves well for this purpose, but if it is not appropriate in a given situation, what options does the analyst have? We review some possibilities and propose a new independence assumption based on the one-switch property. We argue that it is a natural generalization of utility independence and show how it leads to tractable multiattribute utility functions.
66 citations
TL;DR: In this paper, the uncertainty equivalent measure is used to compare expected utility and non-expectation utility theories, showing that expected utility performs well away from certainty, but fails near certainty for about 40% of subjects.
Abstract: There is convincing experimental evidence that Expected Utility fails, but when does it fail, how severely, and for what fraction of subjects? We explore these questions using a novel measure we call the uncertainty equivalent. We nd Expected Utility performs well away from certainty, but fails near certainty for about 40% of subjects. Comparing non-Expected Utility theories, we strongly reject Prospect Theory probability weighting, we support disappointment aversion if amended to allow violations of stochastic dominance, but nd the u-v model of a direct preference for certainty the most parsimonious approach.
51 citations
TL;DR: In this article, a comparative analysis from the points of view of theory and application of the expected utility theory, prospect theory, and regret theory is presented, based on an empirical data set on route choice behavior.
Abstract: Various decision theories have been used to explain travelers' behavior. This paper presents a comparative analysis from the points of view of theory and application of the expected utility theory, prospect theory, and regret theory. The application was based on an empirical data set on route choice behavior with and without information provision. Results show that despite the widespread use of expected utility theory to model travelers' behavior, the use of prospect theory is quite appropriate and promising, especially when information is provided. The reference point plays an important role in the prediction ability of prospect theory. The greatest prediction ability occurs when the reference point is aligned with the observed behavior and thus reinforces the necessity of establishing appropriate and meaningful values. This study empirically shows the potential of alternatives to expected utility theory to capture travelers' behavior better, as in the case of prospect theory under the proposed model spe...
50 citations
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TL;DR: This work develops a new class of utility functions, SAHARA utility, with the distinguishing feature that it allows absolute risk aversion to be non-monotone and implements the assumption that agents may become less risk averse for very low values of wealth.
Abstract: We develop a new class of utility functions, SAHARA utility, with the distinguishing feature that it allows absolute risk aversion to be non-monotone and implements the assumption that agents may become less risk-averse for very low values of wealth. The class contains the well-known exponential and power utility functions as limiting cases. We investigate the optimal investment problem under SAHARA utility and derive the optimal strategies in an explicit form using dual optimization methods. We also show how SAHARA utility functions extend the class of contingent claims that can be valued using indifference pricing in incomplete markets.
33 citations
TL;DR: It is shown that Tsetlin and Winkler's multivariate risk attitudes imply ultramodularity of the utility function, and it is demonstrated that geometric properties of a multivariate utility function can be successfully studied by utilizing an integral function expansion (functional ANOVA).
28 citations
TL;DR: In this paper, the authors present a natural extension of Bayesian decision theory from the domain of individual decisions to group decisions, where each group member accepts the assumptions of subjective expected utility theory with respect to the alternatives from which they must choose, but do not assume, a priori, that the group as a whole accepts those assumptions.
Abstract: This paper presents a natural extension of Bayesian decision theory from the domain of individual decisions to the domain of group decisions. We assume that each group member accepts the assumptions of subjective expected utility theory with respect to the alternatives from which they must choose, but we do not assume, a priori, that the group as a whole accepts those assumptions. Instead, we impose a multiattribute utility independence condition on the preferences of the group with respect to the expected utilities of its actions as appraised by its members. The result is that the expected utility of an alternative for the group is a weighted average of the expected utilities of that alternative for its members. The weights must be determined collectively by the group. Pareto optimality is not assumed, though the result is consistent with Pareto optimality.
27 citations
TL;DR: In this paper, a preference foundation for decision under risk is provided, resulting in a model where probability weighting is linear as long as the corresponding probabilities are not extreme (i.e., 0 or 1).
22 citations
TL;DR: In this article, the authors extend the DM's preferences to be defined on both subjective acts and objective lotteries, and show how one may distinguish optimists from pessimists and separate attitude towards uncertainty from curvature of the utility function over monetary prizes.
Abstract: Savage (1954) provided a set of axioms on preferences over acts that were equivalent to the existence of an expected utility representation. We show that in addition to this representation, there is a continuum of other "expected utility" representations in which for any act, the probability distribution over states depends on the corresponding outcomes. We suggest that optimism and pessimism can be captured by the stake-dependent probabilities in these alternative representations; e.g., for a pessimist, the probability of every outcome except the worst is distorted down from the Savage probability. Extending the DM's preferences to be defined on both subjective acts and objective lotteries, we show how one may distinguish optimists from pessimists and separate attitude towards uncertainty from curvature of the utility function over monetary prizes.
21 citations
TL;DR: This article explored the links between economic and evolutionary theories of optimal choice in risky situations, with particular reference to the relationship between utility and fitness, and argued that the link is strongest between evolution and "nonexpected" utility theory, rather than traditional expected utility theory.
Abstract: The problem of how to make optimal choices in the face of risk (or uncertainty) arises in both economics/decision theory and also evolutionary biology; in the former, ‘optimal’ means utility maximizing, while in the latter it means fitness maximizing. This article explores the links, thematic and formal, between the economic and evolutionary theories of optimal choice in risky situations, with particular reference to the relationship between utility and fitness. It is argued that the link is strongest between evolution and ‘nonexpected’ utility theory, rather than traditional expected utility theory.
21 citations
TL;DR: There is no utility function that is independent of the risks it confronts and that exactly has partial-Kelly strategies as the optimal strategy; and constant relative risk aversion utility is a good approximation to such a utility function, particularly when the investor's edge is small.
Abstract: Partial-Kelly strategies, proposed because full-Kelly strategies that use log of fortune as utility were found to be too risky, are examined from the perspective of maximizing expected utility. The results are as follows: (1) there is no utility function that is independent of the risks it confronts and that exactly has partial-Kelly strategies as the optimal strategy; and (2) constant relative risk aversion utility, with the constant relative risk parameter equal to the reciprocal of the partial-Kelly parameter, is a good approximation to such a utility function, particularly when the investor's edge is small.
TL;DR: This formulation provides a general method for deriving the functional form of a multiattribute utility function under a wide variety of conditions and leads to several new independence concepts such as “boundary independence,” which is a weaker condition than utility independence, and “corner independence", which makes higher-order independence assertions.
Abstract: This paper introduces the notion of a multiattribute utility tree. This graphical representation decomposes the von Neumann--Morgenstern utility of a multiattribute consequence into a sum of products of indifference probability assessments of binary gambles. The utility tree displays the sequence of gambles required to elicit the utility value of a consequence. In addition, it enables the analyst to conduct consistency checks on the indifference assessments provided by the decision maker and to change the order of the assessments based on her comfort level. Once the indifference assessments are provided, the utility value of a consequence can be obtained by direct rollback analysis. On a continuous domain, the utility tree decomposes the functional form of a multiattribute utility function into a sum of products of normalized conditional utility functions. Each attribute in the expansion is conditioned on the boundary values of the attributes expanded before it. This formulation provides a general method for deriving the functional form of a multiattribute utility function under a wide variety of conditions. It also leads to several new independence concepts such as “boundary independence,” which is a weaker condition than utility independence, and “corner independence,” which makes higher-order independence assertions. Reversing the order of the nodes in the tree relates several widely used notions of utility independence found in the literature.
TL;DR: This paper relates the multivariate risk aversion concept, which involves the mixed partial derivative of the utility function, to the Arrow--Pratt risk aversion function, and shows that for additive value functions, a decision maker is multivariaterisk averse if and only if he is risk averse over value in the Arrow-Pratt sense.
Abstract: The cross derivatives of a multiattribute utility function play an important role in the choice between multivariate lotteries and in multiattribute Taylor expansions of the utility function. This paper decomposes the cross derivatives into two components: the derivatives of a single-attribute utility function over value and the cross derivatives of the value function. This approach provides a simple method for reasoning about the signs of the cross derivatives of a multiattribute utility function using derivatives of a univariate utility function and the properties of the value function. To illustrate the approach, we relate the multivariate risk aversion concept, which involves the mixed partial derivative of the utility function, to the Arrow--Pratt risk aversion function. We show that for additive value functions, a decision maker is multivariate risk averse if and only if he is risk averse over value in the Arrow--Pratt sense. For other value functions, however, a decision maker can be risk averse or risk seeking over value and still exhibit multivariate risk aversion. The approach also derives the conditions on the value function that relate two important classes of utility functions: single attribute utility functions whose derivatives alternate in sign and multiattribute utility functions whose cross derivatives alternate in sign. These two classes are widely used in practice and form the basis of univariate and multivariate stochastic dominance. Several examples illustrate the approach.
TL;DR: In this article, the authors prove a formula for the computation of optimal financial investments in an expected utility framework with arbitrary (not necessarily concave) utility functions, where the utility function has a convex-concave shape.
Abstract: We prove a formula for the computation of optimal financial investments in an expected utility framework with arbitrary (not necessarily concave) utility functions. This extends classical results on optimal financial investments for strictly concave utility functions and is of importance particularly for applications of prospect theory where the utility function has a convex-concave shape.
TL;DR: In this article, an experiment with a group of 236 Australian superannuation investors to derive an expected utility function for risk and return, and the resulting indifference curves was carried out and the authors concluded that the expected utility functions are consistent with that anticipated in Markowitz [1952] and Sharpe [1964] except that the investors did not consider time horizon.
Abstract: This paper reports on an experiment with a group of 236 Australian superannuation investors to derive an expected utility function for risk and return, and the resulting indifference curves. The paper concludes that the expected utility function is consistent with that anticipated in Markowitz [1952] and Sharpe [1964] except that the investors did not consider time horizon. The paper argues that the analysis of investor behavior is best served by considering the behavior of a group as a whole rather than investors as individuals, and by assessing their choices when faced with successive similar tasks.
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24 Aug 2011
TL;DR: In this paper, the authors address some of the foundational issues of adaptive utility as seen from the perspective of a Bayesian statistician, and explore the implications that such a generalisation has upon the traditional utility concepts of value of information and risk aversion.
TL;DR: The conditions under which all these approaches for evaluating information in expected utility theory agree in a generic decision environment where the decision maker may choose to acquire arbitrary information bundles are discussed.
TL;DR: In this article, a theory of subjective expected utility based on primitives only involving the fact that an act can be judged either "attractive" or "unattractive", is proposed.
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TL;DR: In this paper, the authors provide a formal justification for the existence of subjective random components intrinsic to the outcome evaluation process of decision makers and explicitly assumed in the stochastic choice literature.
Abstract: This paper provides a formal justification for the existence of subjective random components intrinsic to the outcome evaluation process of decision makers and explicitly assumed in the stochastic choice literature. We introduce the concepts of admissible error function and generalized certainty equivalent, which allow us to analyze two different criteria, a cardinal and an ordinal one, when defining suitable approximations to expected utility values. Contrary to the standard literature requirements for irrational preferences, adjustment errors arise in a natural way within our setting, their existence following directly from the disconnectedness of the range of the utility functions. Conditions for the existence of minimal errors are also studied. Our results imply that neither the cardinal nor the ordinal criterion do necessarily provide the same evaluation for two or more different prospects with the same expected utility value. As a consequence, a rational decision maker may define two different generalized certainty equivalents when presented with the same prospect in two different occasions.
TL;DR: In this article, the authors aim to find a generalized value function that will make the value function introduced by Kahneman-Tversky (1992) a special case, which will determine the appropriate parameter of the values function.
Abstract: The Cumulative Prospect Theory (CPT) uses piecewise value functions instead of consumer utility and provides alternative assumptions for investment behaviour approximated by power value function. In this study, our aim to find a generalized value function that will make the value function introduced by Kahneman–Tversky (1992) a special case. This functional form of the value function determine the appropriate parameter of the values function. We believe that if one can approximate the original CPT value function by other types of functions, the optimization problem and the many other implications can be compared to choose the best model depending on the focus of the problems. This, eventually, could result in improving the theory in both theoretical and empirical points of views.
TL;DR: In this article, it was shown that any affine preference order which is monotone with respect to the first stochastic order admits a representation in terms of an expected utility for some nondecreasing utility function.
TL;DR: How is information integrated across the attributes of an option when making risky choices?
Abstract: How is information integrated across the
attributes of an option when making risky
choices? In most descriptive models of
decision under risk, information about
risk, and reward is combined multiplicatively
(e.g., expected value; expected utility
theory, Bernouli, 1738/1954; subjective
expected utility theory, Savage, 1954;
Edwards, 1955; prospect theory, Kahneman
and Tversky, 1979; rank-dependent utility,
Quiggin, 1993; decision field theory,
Busemeyer and Townsend, 1993; transfer
of attention exchange model, Birnbaum,
2008). That is, (some transform of) probability
is multiplied by (some transform of)
reward to give a value for a risky prospect,
and the prospect with the maximum value
is then chosen.
TL;DR: A simple trick is explained that allows us to use the general existence result provided in Kramkov and Schachermayer to provide the existence of utility maximizers for arbitrary coefficients of relative risk aversion.
Abstract: Karatzas et al. (SIAM J. Control Optim. 29:707–730, 1991) ensure the existence of the expected utility maximizer for investors with constant relative risk aversion coefficients less than one. In this note, we explain a simple trick that allows us to use this result to provide the existence of utility maximizers for arbitrary coefficients of relative risk aversion. The simplicity of our approach is to be contrasted with the general existence result provided in Kramkov and Schachermayer (Ann. Appl. Probab. 9:904–950, 1999).
TL;DR: The authors showed that first-order conditional dependent risk aversion is consistent with the framework of the expected utility hypothesis, and related their results to risk diversification, provide insights into their application in economic and finance examples, and discuss their relation with the stock market participation puzzle.
Abstract: Expected utility functions are limited to second-order (conditional) risk aversion, while non-expected utility functions can exhibit either first-order or second-order (conditional) risk aversion. We extend the concept of orders of conditional risk aversion to orders of conditional dependent risk aversion. We show that first-order conditional dependent risk aversion is consistent with the framework of the expected utility hypothesis. We relate our results to risk diversification, provide insights into their application in economic and finance examples, and discuss their relation with the stock market participation puzzle.
TL;DR: In this paper, an awareness-dependent subjective expected utility was developed by taking unawareness structures introduced in Heifetz, Meier, and Schipper (2006, 2008, 2011a) as primitives in the Anscombe-Aumann approach to subjective expectation.
Abstract: We develop awareness-dependent subjective expected utility by taking unawareness structures introduced in Heifetz, Meier, and Schipper (2006, 2008, 2011a) as primitives in the Anscombe-Aumann approach to subjective expected utility. We observe that a decision maker is unaware of an event if and only if her choices reveal that the event is "null" and the negation of the event is "null". Moreover, we characterize "impersonal" expected utility that is behaviorally indistinguishable from awareness-dependent subject expected utility and assigns probability zero to some subsets of states that are not necessarily events. We discuss in what sense probability zero can model unawareness.
TL;DR: The Ellsberg paradox is often cited as evidence for unknowable "ambiguity" versus computable "risk", and a refutation of the Savage axioms regarding expected utility maximization and the program for revealing subjective or belief-type probabilities as discussed by the authors.
Abstract: The Ellsberg paradox is often cited as evidence for unknowable "ambiguity" versus computable "risk", and a refutation of the Savage axioms regarding expected utility maximization and the program for revealing "subjective" or "belief-type" probabilities. This note argues that researchers have been too quick to embrace the Ellsberg critique as a refutation of standard expected utility theory. First, Ellsberg performed no actual experiments, and in fact recent empirical evidence on the Ellsberg paradox argues against ambiguity. Second, simple explanations for the paradox deserve as much attention as theories that introduce a new concept such as "ambiguity." One such simple explanation is to consider the Ellsberg thought experiment as part of a "meta-experiment" that includes repeated draws, in which case the choices described by Ellsberg are consistent with expected utility theory.
01 Apr 2011
TL;DR: In this article, the preferences over distributions are represented by a differentiable mean-variance utility function if and only if the preference functional is L p -Frechet differentiable and the local utility function is quadratic for all distributions.
Abstract: Mean-variance utility functions exhibiting a certain set of properties underpin a large body of financial and economic theories. This paper provides a firm choice-theoretic foundation for such a function. Under the assumption that preferences over distributions are utility-representable, we show that the preferences can be represented by a differentiable mean-variance utility function if and only if the preference functional is L p -Frechet differentiable (for ) and the local utility function is quadratic for all distributions. Assuming the conditions for such a mean-variance utility function, we further identify easily interpretable necessary and sufficient conditions on the preferences for each of the properties that the mean-variance utility function is commonly assumed to exhibit in applications of the mean-variance approach. In the light of the characterizations, it is also shown that the apparent inconsistency demonstrated by Borch in a mean-variance model can be ruled out by appropriate restrictions on the mean-variance utility function. Copyright 2011 Oxford University Press 2010 All rights reserved, Oxford University Press.
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TL;DR: In this paper, the authors show that assuming a SNP distribution for random consumption provides stability to general equilibrium models as expected utility exists for any value of the marginal rate of substitution over time.
Abstract: Economic growth models under uncertainty and rational agents with CRRA utility have been shown to provide quite fragile explanations of consumers’choice as equlibrium comsumption paths (expected utility) are drastically dependant on distributional assumptions. We show that assuming a SNP distribution for random consumption provides stability to general equilibrium models as expected utility exists for any value of the marginal rate of substitution over time. JEL classi…cation: D80.
26 Jul 2011
TL;DR: An expected utility model is proposed to measure the utility toward fuzzy wealth and some properties and concepts, such as certainty equivalence, are analyzed.
Abstract: An expected utility model is proposed to measure the utility toward fuzzy wealth. Some properties and concepts, such as certainty equivalence are analyzed. Based on maximizing the expected utility, some models are given to consider how to form an optimal portfolio: the first problem on investing in a crisp asset and an uncertainty asset with fuzzy value, the second problem on investing in a set of fuzzy assets. A condition for the existence of optimal portfolio is given.