Mark J. Machina

Temporal risk and the nature of induced preferences

Abstract It has been known since the work of H. Markowitz (“Portfolio Selection: Efficient Diversification of Investments,” Yale Univ. Press, 1959) and J. Mossin (Amer. Econ. Rev. 59 (1969) , 172–174) that even an individual whose underlying preferences satisfy the von Neumann-Morgenstern axioms will not choose over delayed (i.e., “temporal”) risky prospects in a manner which can be modelled as expected utility maximizing. Since most economically important instances of risk taking (insurance, real investment, agriculture, career training) involve delayed as opposed to immediately resolved risk, the standard use of expected utility theory to model such decisions must be questioned. In this paper the technique of “generalized expected utility analysis” ( M. J. Machina, Econometrica 50 (1982) , 277–323) and the theory of support functions ( R. T. Rockafellar, “Convex Analysis,” Princeton Univ. Press, 1970 ) are applied to exactly model and hence determine the nature of preferences over temporal risky prospects.

Decision-making in the presence of risk

Proposed in the 18th century by Cramer and Bernoulli and formally axiomatized in the 20th century by von Neumann and Morgenstern and others, the expected utility model has long been the dominant framework for the analysis of decision-making under risk. A growing body of experimental evidence, however, indicates that individuals systematically violate the key behavioral assumption of this model, the so-called independence axiom. This has led to the development and analysis of nonexpected utility models of decision-making. Although recent work in this area has shown that the analytical results of expected utility theory are more robust than previously supposed, other important issues remain unresolved.

Comparative Statics and Non-expected Utility Preferences*

Abstract Researchers have shown that many, though not all, of the basic results of expected utility analysis can be more or less directly generalized to non-expected utility preferences. This paper describes the essential difference between results which can be extended in this manner and those which cannot and shows that an important family of comparative statics theorems falls into the former class.

Ambiguity and ambiguity aversion

Abstract The phenomena of ambiguity and ambiguity aversion , introduced in Daniel Ellsberg’s seminal 1961 article, are ubiquitous in the real world and violate both the key rationality axioms and classic models of choice under uncertainty. In particular, they violate the hypothesis that individuals’ uncertain beliefs can be represented by subjective probabilities (sometimes called personal probabilities or priors ). This chapter begins with a review of early notions of subjective probability and Leonard Savage’s joint axiomatic formalization of expected utility and subjective probability. It goes on to describe Ellsberg’s classic urn paradoxes and the extensive experimental literature they have inspired. It continues with analytical descriptions of the numerous (primarily axiomatic) models of ambiguity aversion which have been developed by economic theorists, and concludes with a discussion of some current theoretical topics and newer examples of ambiguity aversion.

The Ross characterization of risk aversion: strengthening and extension

This paper offers an interpretive comparison of the Arrow-Pratt and Ross characterizations of comparative risk aversion for expected utility maximizers. The tools used in this comparison are then applied to obtain a strengthening of the Ross cha racterization. This strengthened result is in turn extended to the ca se of general, smooth, nonexpected utility preferences over probabili ty distributions. Copyright 1987 by The Econometric Society.

Expected Utility Hypothesis

The expected utility hypothesis of behaviour towards risk is essentially the hypothesis that the individual decision–maker possesses (or acts as if possessing) a ‘von Neumann-Morgenstern utility function’ U(·) or ‘von Neumann-Morgenstern utility index’ {Ui} defined over some set of outcomes, and when faced with alternative risky prospects or ‘lotteries’ over these outcomes, will choose that prospect which maximizes the expected value of U(·) or {Ui}. Since the outcomes could represent alternative wealth levels, multidimensional commodity bundles, time streams of consumption, or even non–numerical consequences (e.g. a trip to Paris), this approach can be applied to a tremendous variety of situations, and most theoretical research in the economics of uncertainty, as well as virtually all applied work in the field (e.g. optimal trade, investment or search under uncertainty) is undertaken in the expected utility framework.

Chapter 2 Forecasting and Decision Theory

Abstract When forecasts of the future value of some variable, or the probability of some event, are used for purposes of ex ante planning or decision making, then the preferences, opportunities and constraints of the decision maker will all enter into the ex post evaluation of a forecast, and the ex post comparison of alternative forecasts. After a presenting a brief review of early work in the area of forecasting and decision theory, this chapter formally examines the manner in which the features of an agents decision problem combine to generate an appropriate decision-based loss function for that agents use in forecast evaluation. Decision-based loss functions are shown to exhibit certain necessary properties, and the relationship between the functional form of a decision-based loss function and the functional form of the agents underlying utility function is characterized. In particular, the standard squared-error loss function is shown to imply highly restrictive and not particularly realistic properties on underlying preferences, which are not justified by the use of a standard local quadratic approximation. A class of more realistic loss functions (“location-dependent loss functions”) is proposed.

Beliefs, interactions and preferences in decision making

Introduction to the Volume. Part 1: Individual Decision Under Risk and Uncertainty. Subjectively Expected State-Dependent Utility on State-Dependent Consequence Domains P.J. Hammond. Risk and Uncertainty Aversion on Certainty Equivalent Functions A. Montesano. The State-Contingent Approach to Risk Premiums and Comparative Statics in Generalised Expected Utility Theory J. Quiggin, R.G. Chambers. The Preservation of Comparative Statics Under Uncertainty E.E. Schlee. Part 2: Interaction, Information and Beliefs. Non-Additive Beliefs: From Decision to Game Theory H. Haller. A Positive Value of Information for a Non-Bayesian Decision-Maker A. Chassagnon, J.-C. Vergnaud. Preference Summaries for Stochastic Tree Rollback G.B. Hazen, J. Sounderpandian. Do We Really Need Numerous Observations to Select Candidates? (the D-Day Theorem) A. Billot. Education Signalling and Uncertainty J. Eichberger, D. Kelsey. Self-Awareness, Uncertainty and Markets with Overconfidence H.K. Hvide. Part 3: Interaction and Rationality. Combinatoric and Geometric Aspects of Some Probabilistic Choice Models - A Review J.-P. Doignon, et al. Probabilistic Interactions Among Players of a Cooperative Game M. Grabisch, M. Roubens. Arbitrage, Incomplete Models, and Other Peoples Brains R. Nau. Part 4: Experimental Research. Changing Decision Rules: Uncovering Behavioral Strategies Using Estimation/Classification (EC) M.A. El Gamal, D.M. Grether. The Intertemporal Choice Triangle B. Sopher, G. Gigliotti. Testing the Effects of Similarity and Real Payoffs on Choice D. Buschena, D. Zilberman. How Consistent are Probability Tradeoffs in Individual Preferences Under Risk?M. Abdellaoui, B. Munier. Part 5: Applications to Industry and Finance. Symmetrical Monotone Risk Aversion and Positive Bid-Ask Spreads M. Abouda, A. Chateauneuf. Time Resolution and Asymmetric Information: An Application to Financial Markets D. Ami. The Pricing of Optimal Insurance Policies J. Mayer, M.B. Ormiston. Multi-Attribute Decision Making and Generalized Expected Utility in Nuclear Power Plant Maintenance F. Beaudouin, et al. Index.

Moment preferences and polynomial utility

Abstract This paper presents a direct algebraic (i.e., non-calculus) proof of the well-known equivalence of m -moment preferences and m -degree polynomial utility for an expected utility maximizer.

Flexibility and the demand for risky assets

Abstract The fact that reduced flexibility always increases the demand for insurance has led to the belief that reduced flexibility always makes individuals more ‘risk averse’. However, it is quite possible for reduced flexibility to lead to less risk averse behavior in the standard asset demand sense.