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

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"

Cold feet

Individuals often lose confidence in their prospects as they approach the `moment of truth.' An axiomatic model of such individuals is provided. The model adapts and extends (by relaxing the Independence axiom) Gul and Pesendorfer's model of temptation and self-control to capture an individual who changes her beliefs so as to become more pessimistic as payoff time approaches. In a variation of the model, the individual becomes more optimistic at an ex post stage in order to feel better about her available options.Pessimism, optimism, cold feet, temptation, self-control, moment of truth, temporal proximity, confidence

An axiomatic model of 'cold feet'

Individuals often lose confidence in their prospects as they approach the "moment of truth." An axiomatic model of such individuals is provided. The model adapts and extends (by relaxing the Independence axiom) Gul and Pesendorfer's model of temptation and self-control to capture an individual who changes her beliefs so as to become more pessimistic as payoff time approaches. In a variation of the model, the individual becomes more optimistic at an ex post stage in order to feel better about her available options.pessimism, optimism, cold feet, temptation, self-control, moment of truth, temporal proximity, confidence

A Two-Person Dynamic Equilibrium under Ambiguity

This paper describes a pure-exchange, continuous-time economy with two heterogeneous agents and complete markets. A novel feature of the economy is that agents perceive some security returns as ambiguous in the sense often attributed to frank Knight. The equilibrium is described completely in closed-form. In particular, closed-form solutions are obtained for the equilibrium processes describing individual consumption, the interest rate, the market price of uncertainty, security prices and trading strategies. After identifying agents as countries, the model is applied to address the consumption home-bias puzzles.ambiguity, risk, continuous-time, asset returns, Knightian uncertainty, dynamic equilibrium, home bias

Symmetry of evidence without evidence of symmetry

The de Finetti Theorem is a cornerstone of the Bayesian approach. Bernardo (1996) writes that its "message is very clear: if a sequence of observations is judged to be exchangeable, then any subset of them must be regarded as a random sample from some model, and there exists a prior distribution on the parameter of such model, hence requiring a Bayesian approach." We argue that while exchangeability, interpreted as symmetry of evidence, is a weak assumption, when combined with subjective expected utility theory, it implies also complete confidence that experiments are identical. When evidence is sparse, and there is little evidence of symmetry, this implication of de Finetti's hypotheses is not intuitive. This motivates our adoption of multiple-priors utility as the benchmark model of preference. We provide two alternative generalizations of the de Finetti Theorem for this framework. A model of updating is also provided.Ambiguity, exchangeability, symmetry, updating, learning, multiple-priors

Mutual Absolute Continuity of Multiple Priors

This note provides a behavioral characterization of mutually absolutely continuous multiple priors.Mutual absolute continuity, Multiple priors

Non-Bayesian Updating : A Theoretical Framework

This paper models an agent in an infinite horizon setting who does not update according to Bayes' Rule, and who is self-aware and anticipates her updating behavior when formulating plans. Choice-theoretic axiomatic foundations are provided. Then the model is specialized axiomatically to capture updating biases that reflect excessive weight given to (i) prior beliefs, or alternatively, (ii) the realized sample. Finally, the paper describes a counterpart of the exchangeable Bayesian model, where the agent tries to learn about parameters, and some answers are provided to the question "what does a non-Bayesian updater learn?"non-Bayesian updating, overreaction, underreaction, confirmatory bias, law of small numbers, gambler's fallacy, hot hand fallacy, temptation, self-control, learning, menus