Option price without expected utility

We consider the meaning of the option price, commonly acknowledged as the preferred ex ante welfare measure, in the rank-dependent expected utility (RDEU) framework. The importance of this pertains to performing benefit-cost analysis when RDEU maximizers are prevalent in society.     

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.     

Subjective ambiguity, expected utility and Choquet expected utility

Summary. Using the Savage set up, this paper provides a simple axiomatization of the Choquet Expected Utility model where the capacity is an inner measure. Two attractive features of the model are its specificity and the transparency of its axioms. The key axiom states that the decision-maker uses unambiguous acts to approximate ambiguous ones. In addition, the notion of ‘ambiguity’ is subjective and derived from preferences. Received: March 23, 2000; revised version: April 24, 2001     

Lexicographic expected utility with a subjective state space

This paper provides a model that allows for a criterion of admissibility based on a subjective state space. For this purpose, we build a non-Archimedean model of preference with subjective states, generalizing Blume et al. (Econometrica 59:61–79, 1991), who present a non-Archimedean model with exogenous states; and Dekel et al. (Econometrica 69:891–934, 2001), who present an Archimedean model with an endogenous state space. We interpret the representation as modeling an agent who has several “hypotheses” about her state space, and who views some as “infinitely less relevant” than others.     

Is the expected utility maximization hypothesis refutable by finite market data: The case of two observations

It is shown that with only two observations on the asset demand functions of an investor, it is not possible to refute the hypothesis of expected utility maximization on the part of the investor as long as the axioms of revealed preference are satisfied.     

Ambiguous events and maxmin expected utility

We study the properties associated to various definitions of ambiguity [L.G. Epstein, J. Zhang, Subjective probabilities on subjectively unambiguous events, Econometrica 69 (2001) 265-306; P. Ghirardato et al., Differentiating ambiguity and ambiguity attitude, J. Econ. Theory 118 (2004) 133-173; K. Nehring, Capacities and probabilistic beliefs: a precarious coexistence, Math. Soc. Sci. 38 (1999) 197-213; J. Zhang, Subjective, ambiguity, expected utility and Choquet expected utility, Econ. Theory 20 (2002) 159-181] in the context of Maximin Expected Utility (MEU). We show that each definition of unambiguous events produces certain restrictions on the set of priors, and completely characterize each definition in terms of the properties it imposes on the MEU functional. We apply our results to two open problems. First, in the context of MEU, we show the existence of a fundamental incompatibility between the axiom of “Small unambiguous event continuity” (Epstein and Zhang, 2001) and the notions of unambiguous event due to Zhang (2002) and Epstein and Zhang (2001). Second, we show that, in the context of MEU, the classes of unambiguous events according to either Zhang (2002) or Epstein and Zhang (2001) are always λ-systems. Finally, we reconsider the various definitions in light of our findings, and identify some new objects (Z-filters and EZ-filters) corresponding to properties which, while neglected in the current literature, seem relevant to us.     

Effort maximization in asymmetric contest games with heterogeneous contestants

Contest rules are set up by administrators who frequently have discretionary power in specifying the details of these rules, i.e., they can bias the contest rules toward specific contestants in order to further their prime objective. We derive the optimal bias of the contest rule for a contest administrator, who is interested in maximizing the total efforts expended in the contest. The solution is obtained in closed form for a widely used class of n-person contest games. Setting the optimal bias has important implications: (i) there is never exclusion of strong players, instead there is (endogenously induced) inclusion of weak contestants; (ii) the contest administrator will optimally level the playing field by encouraging weak contestants, but he will not equalize the contestants’ chances unless they are identical; and (iii) at least three contestants will be active in equilibrium of the optimal contest, irrespective of heterogeneity.     

Upper and lower bounds for expected utility

Summary.   The decision-theoretic literature has developed very few techniques to bound the expected utility of a random variable when only simple statistics like its median or mode or mean are known. One reason for this lack of results is that we are missing a convenient way to link probability theory and expected utility. This paper is written to demonstrate a general (and genuinely probabilistic) technique to obtain upper and lower bounds for the expected utility of a lottery. Received: December 14, 1999; revised version: March 8, 2000     

Profitability of price and quantity strategies in a duopoly with vertical product differentiation

Using a model according to Mussa and Rosen (1978) and Bonanno and Haworth (1998) we consider a sub-game perfect equilibrium of a two-stage game in a duopolistic industry in which the products of the firms are vertically differentiated. In the industry, there are a high quality firm and a low quality firm. In the first stage of the game, the firms choose their strategic variables, price or quantity. In the second stage, they determine the levels of their strategic variables. We will show that, under an assumption about distribution of consumers' preference, we obtain the result that is similar to Singh and Vives (1984)' proposition (their Proposition 3) in the case of substitutes with nonlinear demand functions. That is, in the first stage of the game, a quantity strategy dominates a price strategy for both firms. Received: April 23, 1999; revised version: May 31, 2000     

More pessimism than greediness: a characterization of monotone risk aversion in the rank-dependent expected utility model

Summary. This paper studies monotone risk aversion, the aversion to monotone, mean-preserving increase in risk (Quiggin [21]), in the Rank Dependent Expected Utility (RDEU) model. This model replaces expected utility by another functional, characterized by two functions, a utility function u in conjunction with a probability-perception function f. Monotone mean-preserving increases in risk are closely related to the notion of comparative dispersion introduced by Bickel and Lehmann [3,4] in Non-parametric Statistics. We present a characterization of the pairs (u,f) of monotone risk averse decision makers, based on an index of greediness G _u of the utility function u and an index of pessimism P _f of the probability perception function f: the decision maker is monotone risk averse if and only if . The index of greediness (non-concavity) of u is the supremum of taken over . The index of pessimism of f is the infimum of taken over 0 < v < 1. Thus, , with G _u = 1 iff u is concave. If then , i.e., f is majorized by the identity function. Since P _f = 1 for Expected Utility maximizers, forces u to be concave in this case; thus, the characterization of risk aversion as is a direct generalization from EU to RDEU. A novel element is that concavity of u is not necessary. In fact, u must be concave only if P _f = 1.Received: 10 April 2001, Revised: 18 November 2003, JEL Classification Numbers: D81. Correspondence to: Michéle CohenAlain Chateauneuf, Michéle Cohen, Isaac Meilijson: We are most grateful to Mark Machina, Peter Wakker and two anonymous referees for very helpful suggestions and comments.     

Is the optimum quantity of money compatible with the unique price level under laissez-faire?

The purpose of this paper is to set forth a general equilibrium model to demonstrate that even if the real social costs of producing money are positive, the optimum quantity of money is incompatible with the unique price level under laissez-faire if zero-degree homogeneity of the production-maintenance cost function in M and P is assumed.     

The subjective expected utility hypothesis and revealed preference

Summary A choice behavior of a decision maker is said to satisfy the subjective expected utility hypothesis if there exist a utility and a subjective probability such that a decision maker chooses acts with the highest expected utility. We present a revealed preference characterization of choice behavior that is consistent with the subjective expected utility hypothesis. Our result applies to any state space and compact sets of prizes and observations (either finite or infinite).     

Constrained sales maximization under a linear technology

This paper employs the activity analysis framework of linear programming to solve the decision problem of maximizing sales revenue in the presence of a minimum acceptable profit constraint. One of the advantages of using this model relative to the standard neoclassical approach is that, in addition to determining the firm's optimal product mix, we can also explore the ramifications of constrained revenue maximization on the imputed valuation of the firm's resources. The primal and dual solution values for the constrained revenue maximization problems are then compared with those derived from a linear profit maximization model. A computational technique is offered which demonstrates how constrained revenue maximization is carried out in actual practice.     

Paying the expected externality for a price quote achieves bargaining efficiency

A seller and buyer have reservation prices x and y. Each has a subjective distribution on the other's reservation price. Paying an offer or the expected benefit the other participant receives from his offer induces honest price quotations, hence efficiency: sale iff y> x.     

Trade openness and child health: a heterogeneous panel cointegration analysis

ABSTRACT

In this paper, we examine the impact of trade openness on child health, based on a cross-country panel data set covering 66 countries for the period 1960–2013. To account for the time-series properties of the data and potential cross-country heterogeneity in the impact of trade openness, the study employs heterogeneous panel cointegration techniques that are robust to omitted variables and endogeneity problems. The results reveal that trade openness and child health are cointegrated, and that trade works to reduce the child mortality rate significantly in the long-run. The results are robust to the methodology and trade openness and child health indicators employed, as well as to the presence of cross-sectional dependence and changes in the sample composition. The findings also suggest that the impact of trade on child health tends to be stronger in countries with better institutional quality, lower corruption, good governance, political stability, and sound policies that promote private sector development.     

The theory of economic price and quantity indicators

Summary. This paper develops the theory of economic price and quantity indicators, being the difference analogue of indexes. The properties of indicators and indexes are compared. Observable bounds for the indicators will be derived, as well as two exactness results for Bennet (1920)-type price and quantity indicators.Received: 3 January 2002, Revised: 2 December 2002, JEL Classification Numbers: C43Previous versions of this paper were presented at the Economic Measurement Group Workshop 2001, School of Economics, University of New South Wales, Sydney, 30 March 2001, and at a seminar at the School of Economics, University of New England, Armidale NSW, 7 September 2001. The authors thank Erwin Diewert for helpful comments on a previous version. The views expressed in this paper do not necessarily reflect any policy of Statistics Netherlands.     

A simple axiomatization and constructive representation proof for choquet expected utility

>P>Summary. We provide a set of simple and intuitive set of axioms that allow for a direct and constructive proof of the Choquet Expected Utility representation for decision making under uncertainty. Received: October 29, 2002; revised version: November 13, 2002 RID="*" ID="*" We thank Matthew Ryan for very useful comments and suggestions on related work and for encouraging us to write this note. Correspondence to: S. Grant     

Commodity price cycles and heterogeneous speculators: a STAR–GARCH model

We propose an empirical commodity market model with heterogeneous speculators. While the power of trend-extrapolating chartists is constant over time, the symmetric impact of stabilizing fundamentalists adjusts endogenously according to market circumstances: Using monthly data for various commodities such as cotton, sugar or zinc, our STAR–GARCH model indicates that their influence positively depends on the distance between the commodity price and its long-run equilibrium value. Fundamentalists seem to become more and more convinced that mean reversion will set in as the mispricing enlarges. Commodity price cycles may thus emerge due to the nonlinear interplay between different trader types. The paper represents the authors’ personal opinion and does not necessarily reflect the views of the Deutsche Bundesbank.