An Axiomatic Model of Non-Bayesian Updating

This paper models an agent in a three-period setting who does not update according to Bayes'Rule, and who is self-aware and anticipates her updating behavior when formulating plans. The agent is rational in the sense that her dynamic behavior is derived from a single stable preference order on a domain of state-contingent menus of acts. A representation theorem generalizes the (dynamic version of) Anscombe-Aumann's theorem so that both the prior and the way in which it is updated are subjective.Bayes' Rule, non-Bayesian updating, asset price volatility, no-trade theorems, agreeing to bet, common knowledge, temptation, self-control, conservatism, representativeness, overconfidence

An Axiomatic Model of Non-Bayesian Updating

This paper models an agent in a three-period setting who does not update according to Bayes'Rule, and who is self-aware and anticipates her updating behavior when formulating plans. The agent is rational in the sense that her dynamic behavior is derived from a single stable preference order on a domain of state-contingent menus of acts. A representation theorem generalizes the (dynamic version of) Anscombe-Aumann's theorem so that both the prior and the way in which it is updated are subjective.Bayes' Rule, non-Bayesian updating, asset price volatility, no-trade theorems, agreeing to bet, common knowledge, temptation, self-control, conservatism, representativeness, overconfidence

Living with risk

Living with risk can lead to anticipatory feelings such as anxiety or hopefulness. Such feelings can a¤ect the choice between lotteries that will be played out in the future - choice may be motivated not only by the (static) risks involved but also by the desire to reduce anxiety or to promote savoring. This paper provides a model of preference in a three-period setting that is axiomatic and includes a role for anticipatory feelings. It is shown that the model of preference can accommodate intuitive patterns of demand for information such as information seeking when a favorable outcome is very likely and information aversion when it is more likely that the outcome will be unfavorable. Behavioral meaning is given to statements such as "individual 1 is anxious" and "2 is more anxious than 1". Finally, the model is di¤erentiated sharply from the classic model due to Kreps and Porteus.risk, anxiety, savoring, anticipatory feelings, demand for commitment, demand for information, temporal resolution of risk, temptation

Optimal learning under robustness and time-consistency

We model learning in a continuous-time Brownian setting where there is prior ambiguity. The associated model of preference values robustness and is time-consistent. It is applied to study optimal learning when the choice between actions can be postponed, at a per-unit-time cost, in order to observe a signal that provides information about an unknown parameter. The corresponding optimal stopping problem is solved in closed form, with a focus on two specific settings: Ellsberg’s two-urn thought experiment expanded to allow learning before the choice of bets, and a robust version of the classical problem of sequential testing of two simple hypotheses about the unknown drift of a Wiener process. In both cases, the link between robustness and the demand for learning is studied.Accepted manuscrip

Ambiguous volatility and asset pricing in continuous time

This paper formulates a model of utility for a continuous time framework that captures the decision-maker's concern with ambiguity about both volatility and drift. Corresponding extensions of some basic results in asset pricing theory are presented. First, we derive arbitrage-free pricing rules based on hedging arguments. Ambiguous volatility implies market incompleteness that rules out perfect hedging. Consequently, hedging arguments determine prices only up to intervals. However, sharper predictions can be obtained by assuming preference maximization and equilibrium. Thus we apply the model of utility to a representative agent endowment economy to study equilibrium asset returns. A version of the C-CAPM is derived and the effects of ambiguous volatility are described

Cognitive Dissonance and Choice

People like to feel good about past decisions. This paper models self- justification of past decisions. The model is axiomatic: axioms are defined on preference over ex ante actions (modeled formally by menus) The representation of preference admits the interpretation that the agent adjusts beliefs after taking an action so as to be more optimistic about its possible consequences. In particular, the ex post choice of beliefs is part of the representation of preference and not a primitive assumption. Behavioral characterizations are given to the comparisons "1 exhibits more dissonance than 2" and "1 is more self-justifying than 2."cognitive dissonance, optimism, temptation, self-control, self-justification, choice-theoretic, choosing beliefs

Learning Under Ambiguity

This paper considers learning when the distinction between risk and ambiguity matters. It first describes thought experiments, dynamic variants of those provided by Ellsberg, that highlight a sense in which the Bayesian learning model is extreme - it models agents who are implausibly ambitious about what they can learn in complicated environments. The paper then provides a generalization of the Bayesian model that accommodates the intuitive choices in the thought experiments. In particular, the model allows decision-makers’ confidence about the environment to change — along with beliefs — as they learn. A calibrated portfolio choice application shows how this property induces a trend towards more stock market participation and investment.ambiguity, learning, noisy signals, ambiguous signals, quality information, portfolio choice, portfolio diversification, Ellsberg Paradox

Ambiguous correlation

Many decisions are made in environments where outcomes are determined by the realization of multiple random events. A decision maker may be uncertain how these events are related. We identify and experimentally substantiate behavior that intuitively reflects a lack of confidence in their joint distribution. Our findings suggest a dimension of ambiguity which is different from that in the classical distinction between risk and "Knightian uncertainty"

Learning Under Ambiguity

This paper considers learning when the distinction between risk and ambiguity (Knightian uncertainty) matters. Working within the framework of recursive multiple-priors utility, the paper formulates a counterpart of the Bayesian model of learning about an uncertain parameter from conditionally i.i.d. signals. Ambiguous signals capture responses to information that cannot be captured by noisy signals. They induce nonmonotonic changes in agent confidence and prevent ambiguity from vanishing in the limit. In a dynamic portfolio choice model, learning about ambiguous returns leads to endogenous stock market participation costs that depend on past market performance. Hedging of ambiguity provides a new reason why the investment horizon matters for portfolio choice.ambiguity, learning, noisy signals, ambiguous signals, quality information, portfolio choice, portfolio diversification, Ellsberg Paradox

Ambiguity, Information Quality and Asset Pricing

When ambiguity averse investors process news of uncertain quality, they act as if they take a worst-case assessment of quality. As a result, they react more strongly to bad news than to good news. They also dislike assets for which information quality is poor, especially when the underlying fundamentals are volatile. These effects induce skewness in asset returns and induce ambiguity premia that depend on idiosyncratic risk in fundamentals. Moreover, shocks to information quality can have persistent negative effects on prices even if fundamentals do not change. This helps to explain the reaction of markets to events like 9/11/2001.ambiguity, information quality, asset pricing, idiosyncratic risk, negatively skewed returns