Expected utility theory from the frequentist perspective

We present an axiomatization of expected utility from the frequentist perspective. It starts with a preference relation on the set of infinite sequences with limit relative frequencies. We consider three axioms parallel to the ones for the von Neumann–Morgenstern (vN–M) expected utility theory. Limit relative frequencies correspond to probability values in lotteries in the vN–M theory. This correspondence is used to show that each of our axioms is equivalent to the corresponding vN–M axiom in the sense that the former is an exact translation of the latter. As a result, a representation theorem is established: The preference relation is represented by an average of utilities with weights given by the relative frequencies.     

Expected utility theory and prospect theory: one wedding and a decent funeral

Choice behavior is typically evaluated by assuming that the data is generated by one latent decision-making process or another. What if there are two (or more) latent decision-making processes generating the observed choices? Some choices might then be better characterized as being generated by one process, and other choices by the other process. A finite mixture model can be used to estimate the parameters of each decision process while simultaneously estimating the probability that each process applies to the sample. We consider the canonical case of lottery choices in a laboratory experiment and assume that the data is generated by expected utility theory and prospect theory decision rules. We jointly estimate the parameters of each theory as well as the fraction of choices characterized by each. The methodology provides the wedding invitation, and the data consummates the ceremony followed by a decent funeral for the representative agent model that assumes only one type of decision process. The evidence suggests support for each theory, and goes further to identify under what demographic domains one can expect to see one theory perform better than the other. We therefore propose a reconciliation of the debate over two of the dominant theories of choice under risk, at least for the tasks and samples we consider. The methodology is broadly applicable to a range of debates over competing theories generated by experimental and non-experimental data.     

Expected utility inequalities: theory and applications

Suppose we know the utility function of a risk averse decision maker who values a risky prospect X at a price CE. Based on this information alone I develop upper bounds for the tails of the probabilistic belief about X of the decision maker. In the paper I also illustrate how to use these expected utility bounds in a variety of applications, which include the estimation of risk measures from observed data, option valuation, and the study of credit risk. I would like to thank John Cochrane, Tom Cosimano, Amanda Friedenberg, George Korniotis, Markus Brunermeier and Paul Schultz for helpful discussions and to participants at two Notre Dame seminars, at the 2006 Spring Midwest Economic Theory and International Economics Conference, and at the 2006 Australasian Meeting of the Econometric Society for their very useful comments. I began working on this project during a year-long visit to the Central Bank of Venezuela. I gratefully acknowledge their hospitality and financial support.     

A theory of anticipated utility

A new theory of cardinal utility, with an associated set of axioms, is presented. It is a generalization of the von Neumann-Morgenstern expected utility theory, which permits the analysis of phenomena associated with the distortion of subjective probability.     

Dominance in SSB utility theory

SSB utility theory represents preferences between probability measures by the positive part of a skew-symmetric bilinear functional φ defined on pairs of measures. Three facets of the theory are examined. First, dominance axioms are used to extend φ to an integral form. Second, the maximizing behavior of φ on subspaces of measures is investigated. Third, aspects of stochastic dominance are explored in the SSB setting.     

Quasi-indifference classes in utility theory

Summary Although the indifference classes of a strictly monotonie preference relation defined on the positive orthant ofn-space do not always separate, one can always construct quasi-indifference classes which do. In many cases the quasi-indifference classes coincide with the indifference classes but, in general, two quasi-indifference classes can intersect. It has been asserted that, on economic grounds, this does not normally happen; here, we examine this assertion from a mathematical point of view.     

Expected utility theory and the experiments

The experimental evidence against expected utility theo or unconvincing. When one modifies the experiments to mi tends to support traditional theory.Dewey H. Johnson Professor of Economics, Department of Economics, College of Business Administration, University of South Carolina. I am grateful for comments from seminar participants at the University of Melbourne, University of South Carolina, University of Stockholm, and the University of Western Ontario. John Hey provided a firm, but sympathetic, editorial hand.     

Testable implications of subjective expected utility theory

I show that the predictive content of the hypothesis of subjective expected utility maximization critically depends on what the analyst knows about the details of the problem a particular decision maker faces. When the analyst does not know anything about the agent's payoffs or beliefs and can only observe the sequence of actions taken by the decision maker any arbitrary sequence of actions can be implemented as the choice of an agent that solves some intertemporal utility maximization problem under uncertainty.     

Testable implications of subjective expected utility theory

I show that the predictive content of the hypothesis of subjective expected utility maximization critically depends on what the analyst knows about the details of the problem a particular decision maker faces. When the analyst does not know anything about the agent's payoffs or beliefs and can only observe the sequence of actions taken by the decision maker any arbitrary sequence of actions can be implemented as the choice of an agent that solves some intertemporal utility maximization problem under uncertainty.     

Decision weights in anticipated utility theory: Response to Segal

The Anticipated Utility model permits the incorporation of decision weights into a model of choice under uncertainty which maintains the desirable properties of transitivity and preservation of dominance. In order to model choice it is necessary to impose appropriate conditions on the decision weighting function. Segal has argued that the function should be concave so that less favorable outcomes are always given more weight than the favorable ones. In this paper it is argued that outlying low probability events, whether favorable or unfavorable, are likely to be ‘overweighted’.     

Investor sentiment and the financial crisis: a sentiment-based portfolio theory perspective

The article proposes a portfolio model subjected to a constraint that captures the investor’s goal, with maximum estimation of expected return that is affected by investor sentiment. And we give a solution of the portfolio model by exploring the geometric features. Furthermore, we discuss the relationship between investor sentiment and the financial crisis by analysing the optimal allocation. The results show that: when investor sentiment is low enough, the investor should reject the investment, this condition leads the depression financial market to prevail, then the financial crisis erupts; when investor sentiment is modest, the financial crisis is difficult to erupt unless the decline of investor sentiment is quick and deep; but there is a special status that the financial crisis is caused by other factors rather than by investor sentiment; and only improving investor sentiment cannot move away from the financial crisis.     

The Austrian theory of the marginal use and of ordinal marginal utility

Conclusion The Austrian theory of the marginal use raises almost as many problems as it has solved. We list here a few of these unsolved problems.Complementarity and rivalness do lead to the ALEP criterion in the examples we worked out above, but we have made no attempt to formalize this rule into a general theorem. Intuitively, the ALEP condition must appear when the complementary or rival relationships are somehow active in the inner or outer marginal uses, but it is not clear exactly what the circumstances are under which this holds.Although the theory leads to quasi-concavity of commodity preferences over goods in the particular cases we worked out, even when rival or complementary interactions are present, it has only been proven that this must be generally true when there are two goods, and then only in the case when the two goods are independent. Perhaps preferences do not really have to be quasi-concave after all.And finally, it must be resolved whether the possibility of intrinsically ordinal preferences nullifies the von Neumann-Morgenstern axiom system, or if instead the validity of those axioms rules out intrinsically ordinal preferences.After over a century, the Austrian theory is still in its youth. Perhaps the day has come for Felix Kaufmann's youngGrenznutzler to return from the netherworld of economic doctrine: There I will quietly lie in wait, Amid my neglected writings, Until I hear the trumpet call of Complementary Goods. Then through the sky will gallop Böhm-Bawerk, Polemics will thunder and flash! Then armed with a quill I'll rise up from the grave, To fight for theGrenznutzen school!²⁷ The author is Scherman Research Fellow at NBER-West and Assistant Professor at Boston College. He is grateful for helpful suggestions made by J. R. Meginniss and by various participants in seminars at Boston College, at the Universities of Hartford and Chicago, at Stanford University, and at NBER-West.     

Cost utility of palivizumab prophylaxis among pre-term infants in the United States: a national policy perspective

Abstract

Objective:

The cost-effectiveness of palivizumab has previously been reported among certain guideline-eligible, high-risk premature infants in Medicaid. Because guideline authorities base decisions on a national perspective, the economic model of palivizumab was adapted to include all infants, that is, public and privately insured patients (60% of palivizumab use is public, 40% is private).

Methods:

This study examined four groups of premature infants without chronic lung disease of prematurity or congenital heart disease: (1) <32 weeks gestational age (wGA) and ≤6 months chronologic age (CA); (2) 32–34 wGA, ≤3 months CA, with 2009 American Academy of Pediatrics (AAP) risk factors (RFs); (3) 32–35 wGA, ≤6 months CA, with 2006 AAP RFs; and (4) 32–35 wGA, ≤6 months CA, with ≤1 RF. An average estimate was used between public and private payors for (1) background rates of respiratory syncytial virus hospitalization (RSV-H), (2) direct medical costs associated with RSV-H, and (3) cost of palivizumab. Incremental cost-effectiveness ratios (ICERs) are reported in cost per quality-adjusted life-year (QALY) gained. Sensitivity analyses were performed.

Results:

Palivizumab saved costs and improved QALYs among infants <32 wGA. Palivizumab was cost-effective in infants 32–34 wGA with 2009 AAP RFs ($44,774 per QALY) and in infants 32–35 wGA with 2006 AAP RFs ($79,477 per QALY). The ICER for infants 32–35 wGA with ≤1 RF was $464,476 per QALY. Influential variables in the sensitivity analysis included background rate of RSV-H and cost and efficacy of palivizumab.

Limitations:

The results are not generalizable to populations outside of the US. The model did not examine all RFs. The wholesale acquisition cost was used as a payment benchmark; actual price paid by end providers varies.

Conclusions:

From a national policy perspective, palivizumab remained cost-effective for publically and commercially insured, guideline-eligible, high-risk premature infants. Palivizumab was not cost-effective in infants of 32–35 wGA with ≤1 RF.     

Background risk in generalized expected utility theory

Summary. In this paper, it is shown that, for a wide range of risk-averse generalized expected utility preferences, independent risks are complementary, contrary to the results for expected utility preferences satisfying conditions such as proper and standard risk aversion. Received: August 10, 2001; revised version: June 18, 2002 RID="*" ID="*"I thank Simon Grant and an anonymous referee for helpful comments and criticism. This research was supported by an Australian Research Council Senior Fellowship and Australian Research Council Large Grant A79800678.     

Expected utility theory without the completeness axiom

We study the problem of obtaining an expected utility representation for a potentially incomplete preference relation over lotteries by means of a set of von Neumann-Morgenstern utility functions. It is shown that, when the prize space is a compact metric space, a preference relation admits such a multi-utility representation provided that it satisfies the standard axioms of expected utility theory. Moreover, the representing set of utilities is unique in a well-defined sense.     

Subjective expected utility theory with costly actions

This paper explores alternative axiomatizations of subjective expected utility theory for decision makers with direct preferences over actions; including a general subjective expected utility representation with action-dependent utility, and separately additive representations. In the context of the state-space formulation of agency theory, the results of this paper constitute axiomatic foundations of the agent's behavior.