CEU Preferences and Dynamic Consistency

This paper investigates the dynamic consistency of CEU preferences. A decision maker is faced with an information structure represented by a fixed filtration. If beliefs are represented by a convex capacity, we show that a necessary and sufficient condition for dynamic consistency is that beliefs be additive over the final stage in the filtration.

Dynamically consistent CEU preferences

We give an axiomatic foundation to the updating rule proposed by [Sarin, R. and Wakker, P. P. (1998). Revealed likelihood and knightian uncertainty. Journal of Risk and Uncertainty 16(3):223-250.] for CEU preferences. This rule is dynamically consistent but non-consequentialist, since forgone consequences are relevant for conditioning. Whereas it does not work universally, but only when counterfactuals outcomes are better and/or worse than the ones resulting on the conditioning event, the rule has many interesting features, since it is able to describe Ellsbergtype preferences together with a recursive structure of the criterion

CEU preferences and dynamic consistency

This paper investigates the dynamic consistency of CEU preferences. A decision maker is faced with an information structure represented by a fixed filtration. If beliefs are represented by a convex capacity, we show that a necessary and sufficient condition for dynamic consistency is that beliefs be additive over the final stage in the filtration

Attitude toward information and learning under multiple priors

This paper studies learning under multiple priors by characterizing the decision maker's attitude toward information. She is incredulous if she integrates new information with respect to only those measures that minimizes the likelihood of the new information and credulous if she uses the maximum likelihood procedure to update her priors. Both updating rules expose her to dynamic inconsistency. We explore different ways to resolve this problem. One way consists to assume that the decision maker's attitude toward information is not relevant to characterize conditional preferences. In this case, we show that a necessary and sufficient condition, introduced by [Epstein L. and Schneider M., 2003. Recursive multiple priors. Journal of Economic Theory 113, 1-31], is the rectangularity of the set of priors. Another way is to extend optimism or pessimism to a dynamic set-up. A pessimistic (max-min expected utility) decision maker will be credulous when learning bad news but incredulous when learning good news.Conversely, an optimistic (max-max expected utility) decision maker will be credulous when learning good news but incredulous when learning bad news. It allows max-min (or max-max) expected utility preferences to be dynamically consistent but it violates consequentialism because conditioning works with respect to counterfactual outcomes. The implications of our findings when the set of priors is the core of a non-additive measure are explored.Multiple priors ; Learning ; Dynamic consistency ; Consequentialism ; Attitude toward information

Investment Behavior under Ambiguity: The Case of Pessimistic Decision Makers

We define pessimistic, respectively optimistic, investors as CEU (Choquet expected utility) decision makers who update their pessimistic, respectively optimistic, beliefs according to a pessimistic (Dempster-Shafer), respectively optimistic, update rule. This paper then demonstrates that, in contrast to optimistic investors, pessimistic investors may strictly prefer investing in an illiquid asset to investing in a liquid asset. Key to our result is the dynamic inconsistency of CEU decision making, implying that a CEU decision maker ex ante prefers a different strategy with respect to prematurely liquidating an uncertain long-term investment project than after learning her liquidity needs. Investing in an illiquid asset then serves as a commitment device guaranteeing an ex ante favorable outcome.

Neo-additive capacities and updating

This note shows that capacities satisfying the axioms consquentialism, state independence and conditional certainty equivalent consistency under updating are a generalised version of neoadditive capacities as axiomatised in Chateauneuf, Eichberger, and Grant (2007)

On attitude polarization under Bayesian learning with non-additive beliefs

Ample psychological evidence suggests that people’s learning behavior is often prone to a "myside bias" or "irrational belief persistence" in contrast to learning behavior exclusively based on objective data. In the context of Bayesian learning such a bias may result in diverging posterior beliefs and attitude polarization even if agents receive identical information. Such patterns cannot be explained by the standard model of rational Bayesian learning that implies convergent beliefs. As our key contribution, we therefore develop formal models of Bayesian learning with psychological bias as alternatives to rational Bayesian learning. We derive conditions under which beliefs may diverge in the learning process despite the fact that all agents observe the same - arbitrarily large - sample, which is drawn from an "objective" i.i.d. process. Furthermore, one of our learning scenarios results in attitude polarization even in the case of common priors. Key to our approach is the assumption of ambiguous beliefs that are formalized as non-additive probability measures arising in Choquet expected utility theory. As a specific feature of our approach, our models of Bayesian learning with psychological bias reduce to rational Bayesian learning in the absence of ambiguity.Non-additive Probability Measures, Choquet Expected Utility Theory, Bayesian Learning, Bounded Rationality

Asset pricing in a Lucas "fruit-tree' economy with non-additive beliefs

We study a Lucas (1978) "fruit-tree" economy under the assumption that agents are Choquet expected utility (CEU) rather than standard expected utility (EU) decision makers. The agents’ non-additive beliefs about the economy’s stochastic dividend payment process may thus express ambiguity attitudes and accommodate violations of Savage’s sure-thing principle as elicited by Ellsberg (1961). As our main formal result we establish the existence of a unique stationary equilibrium price function for the assets in this economy. In order to account for the dynamic inconsistency of CEU decision makers, we thereby use an equilibrium concept that combines the market clearing condition of general equilibrium theory with Bayesian Nash equilibrium. A simple example about the equity premium in our economy with non-additive beliefs illustrates our formal findings.Non-additive Probability Measures, Choquet Expected Utility The- ory, Dynamic Inconsistency, Asset Pricing, Equity Premium Puzzle

Probabilistic sophistication and multiple priors.

We show that under fairly mild conditions, a maximin expected utility preference relation is probabilistically sophisticated if and only if it is subjective expected utility.

When is ambiguity-attitude constant?

Pre-print version. The final publication is available at Springer via http://dx.doi.org/10.1007/s11166-012-9153-5This paper studies how updating affects ambiguity attitude. In particular we focus on generalized Bayesian updating of the Jaffray-Philippe sub-class of Choquet Expected Utility preferences. We find conditions for ambiguity attitude to be the same before and after updating. A necessary and sufficient condition for ambiguity attitude to be unchanged when updated on an arbitrary event is for the capacity to be neo-additive. We find a condition for updating on a given partition to preserve ambiguity attitude. We relate this to necessary and sufficient conditions for dynamic consistency. Finally, we study whether ambiguity increases or decreases after updating.Research supported in part by a Leverhulme Research Fellowship