Ambiguity Averse Agents Research Articles

Bias and Sensitivity under Ambiguity

This paper characterizes the effects of ambiguity aversion under dispersed information. The equilibrium outcome is observationally equivalent to a Bayesian forecast of the fundamental with increased sensitivity to signals and a pessimistic bias. This equivalence result takes a simple form that accommodates dynamic information and strategic interactions. Applying the result, we show that ambiguity aversion helps rationalize the joint empirical pattern between the bias and persistence of inflation forecasts conditional on household income. In a policy game à la Barro and Gordon (1983) with ambiguity-averse agents, the policy rule features higher average inflation and increased responsiveness to fundamentals. (JEL D81, D83, E31, E37, E71)

Ambiguity and informativeness of (non-)trading

We study a sequential trading mechanism with ambiguity-averse agents modeled by multiple prior preferences. Informed traders generally mix between trading and non-trading, and their trading probability decreases with ambiguity. If agents are sufficiently ambiguous, informed traders do not trade, and only noise traders place orders; trading becomes uninformative. When signal accuracy is ambiguous, trading can make public beliefs more ambiguous over time, which leads to social learning failures in the long run. Moreover, since informed traders may not trade, no-trade can also be informative when signal accuracy is asymmetric. Even with continuous action spaces, sufficiently high ambiguity stops social learning.

Social comparison with ambiguity: An investment and consumption game

This study presents an investment and consumption model with two ambiguity-averse agents whose utility depends on the opponent’s consumption. In Nash equilibrium, social comparison increases (decreases) investment and consumption for the more (less) ambiguous agent, decreasing the magnitude difference between agents. The opponent’s reduced ambiguity increases the agent’s investment and consumption by comparison incentive. However, neither rival’s ambiguity level nor comparative motivation affects the agent’s welfare in our one-period model, distinguished from conclusions in continuous time. These results have important implications for the literature about social comparison and ambiguity.

Ambiguous information and dilation: An experiment

With standard models of updating under ambiguity, new information may increase the amount of relevant ambiguity: the set of beliefs may ‘dilate.’ We experimentally test one sharp case: agents bet on a risky urn and get information that is truthful or not based on the draw from an Ellsberg urn. With common models, the set of beliefs dilates, and the value of bets decreases for ambiguity-averse agents and increases for ambiguity-seeking ones. Instead, we find that the value of bets does not change for ambiguity-averse individuals, while it increases substantially for ambiguity-seeking ones. We also test bets on ambiguous urns, in which case we find sizable reactions to ambiguous information.

Mixed strategies and preference for randomization in games with ambiguity averse agents

We study the use of mixed strategies in games by ambiguity averse agents with a preference for randomization. Applying the decision theoretic model of Saito (2015) to games, we establish that the set of rationalizable strategies grows larger as preference for randomization weakens. An agent's preference for randomization is partially observable: given the behavior of an agent in a game, we can determine an upper bound on the strength of randomization preference for that agent. Notably, data in previous experiments on ambiguity aversion in games is not consistent with a maximal preference for randomization for approximately 30% of subjects.

Maxmin implementation

This paper studies the implementation problem of a mechanism designer with ambiguity averse agents. The mechanism designer, desiring to implement a choice correspondence, can create ambiguity for agents by committing to multiple allocation rules and transfer schemes without revealing which one to use. By extending the cyclical monotonicity condition from choice functions to choice correspondences, we show that the condition can fully characterize implementable choice correspondences. We then study the implementability of choice correspondences in supermodular environments. As an application, we consider a mechanism designer who wants to allocate one object to one of her most desired agents and show that she can strictly benefit from concealing the tie-breaking rules. An intuitive and computationally tractable condition is provided to characterize when the mechanism designer's preference induces an implementable choice correspondence.

Can unpredictable risk exposure be priced?

We study the link between beta predictability and the price of risk. An investor who desires exposure to a certain risk factor needs to predict what next period’s beta will be. We use a simple model to show that an ambiguity averse agent’s demand is lower when betas are hard to predict, leading to a reduction in risk premiums. We test the implications for downside betas and VIX betas. We find that they have economically and statistically small prices of risk once we account for the fact that an investor cannot observe ex-post realized betas when determining asset demand.

Incentive compatibility under ambiguity

The paper examines notions of incentive compatibility in an environment with ambiguity-averse agents. In particular, we propose the notion of maxmin transfer coalitional incentive compatibility, which is immune to coalitional manipulations and thus more stable than the individual incentive compatibility condition. The main result characterizes the set of allocations that satisfy the maxmin transfer coalitional incentive compatibility condition. We show that an allocation satisfies maxmin transfer coalitional incentive compatibility if and only if it is maxmin interim efficient. This result extends that of De Castro and Yannelis (J Econ Theory 177:678–707, 2018) in the sense that ambiguity not only resolves the conflict between efficiency and incentive compatibility, it also accommodates stability. Furthermore, this result is false in a finite economy where agents are subjective expected utility maximizers.

Ambiguity, Nominal Bond Yields, and Real Bond Yields

This paper presents an equilibrium bond-pricing model that jointly explains the upward-sloping nominal and real yield curves and the violation of the expectations hypothesis. Instead of relying on the inflation risk premium, the ambiguity-averse agent faces different amounts of Knightian uncertainty in the long run versus the short run; hence the model-implied nominal and real short rate expectations are upward-sloping under the agent’s worst-case equilibrium beliefs. The expectations hypothesis roughly holds under investors’ worst-case beliefs. The difference between the worst-case scenario and the true distribution makes realized excess returns on long term bonds predictable.

Evaluating Optimal Stopping Problems Under Multivariate Settings and Model Uncertainty

In this article we study the evaluation of American options with stochastic volatility models and the optimal fish harvesting decision with stochastic convenience yield models, in the presence of drift ambiguity. From the perspective of an ambiguity averse agent, we transfer the problem to the solution of a reflected backward stochastic differential equations (RBSDE) and prove the uniform Lipschitz continuity of the generator. We then propose a numerical algorithm with the theory of RBSDEs and a general stratification technique, and an alternative algorithm without using the theory of RBSDEs. We test the accuracy and convergence of the numerical schemes. By comparing to the one dimensional case, we highlight the importance of the dynamic structure of the agent’s worst case belief. Results also show that the numerical RBSDE algorithm with stratification is more efficient when the optimal generator is attainable.

Can Unpredictable Risk Exposure Be Priced?

We study the link between beta predictability and the price of risk. An investor who desires exposure to a certain risk factor needs to predict what next period's beta will be. We use a simple model to show that an ambiguity averse agent's demand is lower when betas are hard to predict, leading to a reduction in risk premiums. We test the implications for downside betas and VIX betas. We find that they have economically and statistically small prices of risk once we account for the fact that an investor cannot observe ex-post realized betas when determining asset demand.

Time-varying ambiguity, credit spreads, and the levered equity premium

This paper studies the effects of time-varying Knightian uncertainty (ambiguity) on asset pricing in a Lucas exchange economy. Specifically, it considers a general equilibrium model where an ambiguity-averse agent applies a discount rate that is adjusted not only for the current magnitude of ambiguity but also for the risk associated with its future fluctuations. As such, both the ambiguity level and volatility help to raise the asset premiums and accommodate richer dynamics of asset prices. Based on a novel empirical measure of the ambiguity level, the estimated model can capture the empirical levels of corporate credit spreads and the equity premium while endogenously matching the historical default probability. More importantly, the model-implied credit spread and equity price-dividend ratio perform remarkably in tracking the time variations in their historical counterparts.

Ambiguity and endogenous discounting

Existing work has shown that ambiguity averse agents dislike positive autocorrelation in their consumption profile. Remarkably, the same prediction can be generated by expected-utility models with endogenous discounting if one makes the common assumption of increasing marginal impatience. This paper disentangles the intertemporal predictions of ambiguity aversion from those of endogenous discounting by identifying a form of autocorrelation that is disliked by ambiguity averse agents only. The analysis is supplemented by two representation theorems. The first delivers a novel axiomatization of endogenous discounting without restricting beliefs to be expected utility. Leveraging our analysis of ambiguity aversion, the second result delivers a maxmin representation of beliefs.

Discriminating Between Models of Ambiguity Attitude: a Qualitative Test

AbstractDuring recent decades, many new models have emerged in pure and applied economic theory according to which agents’ choices may be sensitive to ambiguity in the uncertainty that faces them. The exchange between Epstein (2010) and Klibanoff et al. (2012) identified a notable behavioral issue that distinguishes sharply between two classes of models of ambiguity sensitivity that are importantly different. The two classes are exemplified by the α-maxmin expected utility (MEU) model and the smooth ambiguity model, respectively; and the issue is whether or not a desire to hedge independently resolving ambiguities contributes to an ambiguity-averse agent's preference for a randomized act. Building on this insight, we implement an experiment whose design provides a qualitative test that discriminates between the two classes of models. Among subjects identified as ambiguity sensitive, we find greater support for the class exemplified by the smooth ambiguity model; the relative support is stronger among subjects identified as ambiguity averse. This finding has implications for applications that rely on specific models of ambiguity preference.

Ambiguity Aversion in Competitive Insurance Markets with Asymmetric Information

We analyze the effect of ambiguous loss probabilities on competitive insurance markets with asymmetric information. We characterize equilibria under actuarially fair pricing with preferences that are second-order ambiguity averse (have smooth indifference curves). We also show existence of uniqueness of the second-best contracts and provide a characterization. Non-increasing absolute ambiguity aversion is sufficient for adverse selection in the smooth model. We then determine the effect of ambiguity on equilibrium under ambiguity aversion. There is a coverage effect because ambiguity relaxes the self-selection constraint and raises the available coverage for the low risks, and an ambiguity effect because ambiguity makes ambiguity averse agents worse off. Both effects are conflicting when it comes to their impact on the critical pro-portion of high risks required for a Rothschild-Stiglitz equilibrium to exist and social welfare. We derive conditions that allow to resolve the indeterminate social welfare effect.

Ambiguity, Nominal Bond Yields, and Real Bond Yields

This paper presents an equilibrium bond-pricing model that jointly explains the upward-sloping nominal and real yield curves and the violation of the expectations hypothesis. Instead of relying on the inflation risk premium, the ambiguity-averse agent faces different amounts of Knightian uncertainty in the long run versus the short run; hence, the model-implied nominal and real short rate expectations are upward sloping under the agent’s worst-case equilibrium beliefs. The expectations hypothesis roughly holds under investors’ worst-case beliefs. The difference between the worst-case scenario and the true distribution makes realized excess returns on long-term bonds predictable. (JEL D81, D84, E23, E31, E43, E44, G12)

Robust time-inconsistent stochastic control problems

This paper establishes a general analytical framework for continuous-time stochastic control problems for an ambiguity-averse agent (AAA) with time-inconsistent preference, where the control problems do not satisfy Bellman’s principle of optimality. The AAA is concerned about model uncertainty in the sense that she is not completely confident in the reference model of the controlled Markov state process and rather considers some similar alternative models. The problems of interest are studied within a set of dominated models and the AAA seeks for an optimal decision that is robust with respect to model risks. We adopt a game-theoretic framework and the concept of subgame perfect Nash equilibrium to derive an extended dynamic programming equation and extended Hamilton–Jacobi–Bellman–Isaacs equations for characterizing the robust dynamically optimal control of the problem. We also prove a verification theorem to theoretically support our construction of robust control. To illustrate the tractability of the proposed framework, we study an example of robust dynamic mean–variance portfolio selection under two cases: 1. constant risk aversion; and 2. state-dependent risk aversion.

Doubts and variability: A robust perspective on exotic consumption series

Consumption-based asset-pricing models have experienced success in recent years by augmenting the consumption process in ‘exotic’ ways. Two notable examples are the Long-Run Risk and rare disaster frameworks. Such models are difficult to characterize from consumption data alone. Accordingly, concerns have been raised regarding their specification. Acknowledging that both phenomena are naturally subject to ambiguity, we show that an ambiguity-averse agent may behave as if Long-Run Risk and disasters exist even if they do not or exaggerate them if they do. Consequently, prices may be misleading in characterizing these phenomena since they encode a pessimistic perspective of the data-generating process.

IRREVERSIBLE INVESTMENTS AND AMBIGUITY AVERSION

Real option valuation has traditionally been concerned with investment under project value uncertainty while assuming that the agent has perfect confidence in a specific model. However, agents do not generally have perfect confidence in their model and this ambiguity may affect their decisions. In addition, the value of real investments is not typically fully spanned by tradable assets because markets are incomplete as is typically the case in energy and commodities. In this paper, we account for the agent’s aversion to model ambiguity and address market incompleteness through the notion of robust indifference prices. We derive analytical results for the perpetual option to invest and the linear complementarity problem that the finite-time version of this problem satisfies. Ambiguity aversion has a number of effects on decision making some of which cannot be explained by altering the agent’s risk aversion. For example, ambiguity averse agents are found to exercise real options both earlier and later than their ambiguity neutral counterparts, depending on whether ambiguity stems from uncertainty in the dynamics of the project value or the dynamics of a hedging asset.

Innovation and stock market performance: A model with ambiguity-averse agents

Empirical evidence on stock prices shows that firms investing successfully in radical innovation experience higher stock returns. This paper provides a model that sheds light on the relationship between the degree of firm innovativeness and stock returns, the movements of which capture expectations on firm’s profitability and growth. The model is grounding on Neo-Schumpeterian growth models and relies on the crucial assumption of radical innovation, characterized by “ambiguity” or Knightian uncertainty: due to its uniqueness and originality, no distribution of probability can be reasonably associated with radical innovation success or failure. Different preferences (α-maxmin, Choquet) are here compared. Results show that the assumption of ambiguity-aversion is crucial in determining higher returns in the presence of radical innovation and that the specific definition of expected utility shapes the extent of the returns. This result holds also in the case of endogenous innovation; risk attitude plays no role.