Robust Decision Theory and Econometrics

2020 ◽  
Vol 12 (1) ◽  
pp. 239-271 ◽  
Author(s):  
Gary Chamberlain
Keyword(s):  
Decision Theory ◽  
Portfolio Choice ◽  
Expected Utility ◽  
Empirical Work ◽  
Decision Problems ◽  
Maxmin Expected Utility ◽  
The Empirical Analysis ◽  
Variational Preferences ◽  
Constraint Preferences ◽  
Period Model

This review uses the empirical analysis of portfolio choice to illustrate econometric issues that arise in decision problems. Subjective expected utility (SEU) can provide normative guidance to an investor making a portfolio choice. The investor, however, may have doubts on the specification of the distribution and may seek a decision theory that is less sensitive to the specification. I consider three such theories: maxmin expected utility, variational preferences (including multiplier and divergence preferences and the associated constraint preferences), and smooth ambiguity preferences. I use a simple two-period model to illustrate their application. Normative empirical work on portfolio choice is mainly in the SEU framework, and bringing in ideas from robust decision theory may be fruitful.

Ambiguity Models and the Machina Paradoxes

2011 ◽  
Vol 101 (4) ◽  
pp. 1547-1560 ◽  
Author(s):  
AurÉlien Baillon ◽  
Olivier L'Haridon ◽  
Laetitia Placido
Keyword(s):  
Expected Utility ◽  
Ambiguity Aversion ◽  
Choquet Expected Utility ◽  
Maxmin Expected Utility ◽  
Alternative Representation ◽  
Smooth Model ◽  
Variational Preferences

Machina (2009) introduced two examples that falsify Choquet expected utility, presently one of the most popular models of ambiguity. This article shows that Machina's examples falsify not only the model mentioned, but also four other popular models for ambiguity of the literature, namely maxmin expected utility, variational preferences, α-maxmin, and the smooth model of ambiguity aversion. Thus, Machina's examples pose a challenge to most of the present field of ambiguity. Finally, the paper discusses how an alternative representation of ambiguity-averse preferences works to accommodate the Machina paradoxes and what drives the results. (JEL D81)

scholarly journals Risk, rationality and expected utility theory

2015 ◽  
Vol 45 (5-6) ◽  
pp. 798-826 ◽  
Author(s):  
Richard Pettigrew
Keyword(s):  
Decision Theory ◽  
Expected Utility ◽  
Utility Theory ◽  
Expected Utility Theory ◽  
Decision Problems ◽  
Natural Way

There are decision problems where the preferences that seem rational to many people cannot be accommodated within orthodox decision theory in the natural way. In response, a number of alternatives to the orthodoxy have been proposed. In this paper, I offer an argument against those alternatives and in favour of the orthodoxy. I focus on preferences that seem to encode sensitivity to risk. And I focus on the alternative to the orthodoxy proposed by Lara Buchak’s risk-weighted expected utility theory. I will show that the orthodoxy can be made to accommodate all of the preferences that Buchak’s theory can accommodate.

scholarly journals The key to the knowledge norm of action is ambiguity

Synthese ◽  
2021 ◽  
Author(s):  
Patricia Rich
Keyword(s):  
Decision Theory ◽  
Expected Utility ◽  
Utility Theory ◽  
Expected Utility Theory ◽  
Decision Problems ◽  
Epistemic State ◽  
Modeling Tool ◽  
Knowledge Norm ◽  
Knowledge Based

AbstractKnowledge-first epistemology includes a knowledge norm of action: roughly, act only on what you know. This norm has been criticized, especially from the perspective of so-called standard decision theory. Mueller and Ross provide example decision problems which seem to show that acting properly cannot require knowledge. I argue that this conclusion depends on applying a particular decision theory (namely, Savage-style Expected Utility Theory) which is ill-motivated in this context. Agents’ knowledge is often most plausibly formalized as an ambiguous epistemic state, and the theory of decision under ambiguity is then the appropriate modeling tool. I show how to model agents as acting rationally on the basis of their knowledge according to such a theory. I conclude that the tension between the knowledge norm of action and formal decision theory is illusory; the knowledge-first paradigm should be used to actively select the decision-theoretical tools that can best capture the knowledge-based decisions in any given situation.

If It Is Surely Better, Do It More? Implications for Preferences Under Ambiguity

2021 ◽  
Author(s):  
Soheil Ghili ◽  
Peter Klibanoff
Keyword(s):  
Expected Utility ◽  
Ambiguity Aversion ◽  
Upper Bounds ◽  
Maxmin Expected Utility ◽  
Weak Dominance ◽  
Choice Under Uncertainty ◽  
Tight Connection ◽  
Sales Agent ◽  
Utility Preferences ◽  
Sensitive Behavior

Consider a canonical problem in choice under uncertainty: choosing from a convex feasible set consisting of all (Anscombe–Aumann) mixtures of two acts f and g, [Formula: see text]. We propose a preference condition, monotonicity in optimal mixtures, which says that surely improving the act f (in the sense of weak dominance) makes the optimal weight(s) on f weakly higher. We use a stylized model of a sales agent reacting to incentives to illustrate the tight connection between monotonicity in optimal mixtures and a monotone comparative static of interest in applications. We then explore more generally the relation between this condition and preferences exhibiting ambiguity-sensitive behavior as in the classic Ellsberg paradoxes. We find that monotonicity in optimal mixtures and ambiguity aversion (even only local to an event) are incompatible for a large and popular class of ambiguity-sensitive preferences (the c-linearly biseparable class. This implies, for example, that maxmin expected utility preferences are consistent with monotonicity in optimal mixtures if and only if they are subjective expected utility preferences. This incompatibility is not between monotonicity in optimal mixtures and ambiguity aversion per se. For example, we show that smooth ambiguity preferences can satisfy both properties as long as they are not too ambiguity averse. Our most general result, applying to an extremely broad universe of preferences, shows a sense in which monotonicity in optimal mixtures places upper bounds on the intensity of ambiguity-averse behavior. This paper was accepted by Manel Baucells, decision analysis.

Full Implementation under Ambiguity

2021 ◽  
Vol 13 (1) ◽  
pp. 148-178
Author(s):  
Huiyi Guo ◽  
Nicholas C. Yannelis
Keyword(s):  
Social Choice ◽  
Expected Utility ◽  
Sufficient Conditions ◽  
Choice Functions ◽  
Maxmin Expected Utility ◽  
Special Cases ◽  
Social Choice Functions ◽  
Bayesian Implementation ◽  
Pareto Efficient ◽  
Choice Set

This paper introduces the maxmin expected utility framework into the problem of fully implementing a social choice set as ambiguous equilibria. Our model incorporates the Bayesian framework and the Wald-type maxmin preferences as special cases and provides insights beyond the Bayesian implementation literature. We establish necessary and almost sufficient conditions for a social choice set to be fully implementable. Under the Wald-type maxmin preferences, we provide easy-to-check sufficient conditions for implementation. As applications, we implement the set of ambiguous Pareto-efficient and individually rational social choice functions, the maxmin core, the maxmin weak core, and the maxmin value. (JEL D71, D81, D82)

scholarly journals Testing Ambiguity Models through the Measurement of Probabilities for Gains and Losses

2015 ◽  
Vol 7 (2) ◽  
pp. 77-100 ◽  
Author(s):  
Aurélien Baillon ◽  
Han Bleichrodt
Keyword(s):  
Expected Utility ◽  
Ambiguity Aversion ◽  
Choquet Expected Utility ◽  
Maxmin Expected Utility ◽  
Stock Indices ◽  
Descriptive Validity ◽  
Utility Models ◽  
Ambiguity Attitudes ◽  
Gains And Losses ◽  
Fourfold Pattern

This paper reports on two experiments that test the descriptive validity of ambiguity models using a natural source of uncertainty (the evolution of stock indices) and both gains and losses. We observed violations of probabilistic sophistication, violations that imply a fourfold pattern of ambiguity attitudes: ambiguity aversion for likely gains and unlikely losses and ambiguity seeking for unlikely gains and likely losses. Our data are most consistent with prospect theory and, to a lesser extent, α-maxmin expected utility and Choquet expected utility. Models with uniform ambiguity attitudes are inconsistent with most of the observed behavioral patterns. (JEL D81, D83, G11, G12, G14)

scholarly journals Optimal Insurance under Maxmin Expected Utility

2020 ◽  
Author(s):  
Corina Birghila ◽  
Tim J. Boonen ◽  
Mario Ghossoub
Keyword(s):  
Expected Utility ◽  
Maxmin Expected Utility ◽  
Optimal Insurance

scholarly journals Countable additivity, idealization, and conceptual realism

2019 ◽  
Vol 36 (1) ◽  
pp. 127-147
Author(s):  
Yang Liu
Keyword(s):  
Applied Sciences ◽  
Decision Theory ◽  
Expected Utility ◽  
Bayesian Probability ◽  
Subjective Expected Utility ◽  
Countable Additivity ◽  
Mathematical Structures ◽  
Conceptual Realism ◽  
Technical Properties ◽  
Personal Probability

AbstractThis paper addresses the issue of finite versus countable additivity in Bayesian probability and decision theory – in particular, Savage’s theory of subjective expected utility and personal probability. I show that Savage’s reason for not requiring countable additivity in his theory is inconclusive. The assessment leads to an analysis of various highly idealized assumptions commonly adopted in Bayesian theory, where I argue that a healthy dose of, what I call, conceptual realism is often helpful in understanding the interpretational value of sophisticated mathematical structures employed in applied sciences like decision theory. In the last part, I introduce countable additivity into Savage’s theory and explore some technical properties in relation to other axioms of the system.

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