Results 11  20
of
65
Learning and Asset Prices under Ambiguous Information, Forthcoming in Review of Financial Studies
, 2005
"... We propose a new continuous time framework to study asset prices under learning and ambiguity aversion. In a partial information Lucas economy with time additive power utility, a discount for ambiguity arises if and only if the elasticity of intertemporal substitution (EIS) is above one. Then, ambig ..."
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Cited by 18 (1 self)
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We propose a new continuous time framework to study asset prices under learning and ambiguity aversion. In a partial information Lucas economy with time additive power utility, a discount for ambiguity arises if and only if the elasticity of intertemporal substitution (EIS) is above one. Then, ambiguity increases equity premia and volatilities, and lowers interest rates. Very low EIS estimates are consistent with EIS parameters above one, because of a downward bias in Eulerequationsbased least squares regressions. In our setting, ambiguity does not resolve asymptotically and, for high EIS, it is consistent with the equity premium, the low interest rate, and the excess volatility puzzles.
Sharing ambiguity
 American Economic Association Papers and Proceedings 91
, 2001
"... In a version of the Ellsberg Paradox, the decisionmaker is confronted with two urns, each containing 100 balls that are either Red or Blue. She is told that there are 50 of each color in the
rst (unambiguous) urn, but no further information is provided about the second (ambiguous) urn. There is a ..."
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Cited by 18 (0 self)
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In a version of the Ellsberg Paradox, the decisionmaker is confronted with two urns, each containing 100 balls that are either Red or Blue. She is told that there are 50 of each color in the
rst (unambiguous) urn, but no further information is provided about the second (ambiguous) urn. There is a widely exhibited preference to bet on drawing Red (or Blue) from the
rst urn rather than from the second. Though such rankings are intuitive, they are inconsistent with subjective expected utility theory and, more generally, with reliance on any single probability measure to represent beliefs. Thus the Paradox illustrates the behavioral meaning of the Knightian distinction between risk (measurable or probabilistic uncertainty) and ambiguity (unmeasurable uncertainty). The importance of the Ellsberg Paradox is the intuition that this distinction may be important much more widely. In particular, it seems at least plausible to view consumptionsavings and portfolio choice decisions as being qualitatively di¤erent than the choice of which bet to accept on the outcome of a coin ip; only the latter is a choice between risky prospects. My objective in this paper is to illustrate both the tractability and potential fruitfulness (for addressing the homebias puzzle, for example) of a macrostyle model that permits aversion not only to risk but also to ambiguity. I employ a simple twoperiod heterogeneousagent economy. The time periods are t 1 (today) and t (tomorrow). Uncertainty is represented by the state space. There are two consumers and consumer is consumption process is cit1; c
IQ and Stock Market Participation �
, 2009
"... An individual’s IQ stanine, measured early in adult life, is monotonically related to his stock market participation decision later in life. The high correlation between IQ and participation, which exists even among the 10 % most affluent individuals, controls for wealth, income, and other demograph ..."
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Cited by 16 (1 self)
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An individual’s IQ stanine, measured early in adult life, is monotonically related to his stock market participation decision later in life. The high correlation between IQ and participation, which exists even among the 10 % most affluent individuals, controls for wealth, income, and other demographic and occupational information. Supplemental data from siblings are used with both an instrumental variables approach and paired difference regressions to show that our results apply to both females and males, and that omitted familial and nonfamilial variables cannot account for our findings. IQ also is related to diversification. High IQ investors are more likely to hold mutual funds and larger numbers of stocks, other things equal.
Model Uncertainty and Liquidity
 Review of Economic Dynamics
, 2009
"... Extreme market outcomes are often followed by a lack of liquidity and a lack of trade. This market collapse seems particularly acute for markets where traders rely heavily on a specific empirical model such as in derivative markets like the market for mortgage backed securities or credit derivatives ..."
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Cited by 15 (0 self)
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Extreme market outcomes are often followed by a lack of liquidity and a lack of trade. This market collapse seems particularly acute for markets where traders rely heavily on a specific empirical model such as in derivative markets like the market for mortgage backed securities or credit derivatives. Moreover, the observed behavior of traders and institutions that places a large emphasis on “worstcase scenarios ” through the use of “stress testing ” and “valueatrisk ” seems different than Savage expected utility would suggest. In this paper, we capture modeluncertainty using an Epstein and Wang (1994) uncertaintyaverse utility function with an ambiguous underlying assetreturns distribution. To explore the connection of uncertainty with liquidity, we specify a simple market where a monopolist financial intermediary makes a market for a propriety derivative security. The marketmaker chooses bid and ask prices for the derivative, then, conditional on trade in this market, chooses an optimal portfolio and consumption. We explore how uncertainty can increase
SYMMETRY OF EVIDENCE WITHOUT EVIDENCE OF SYMMETRY
, 2008
"... The de Finetti Theorem is a cornerstone of the Bayesian approach. Bernardo [4, p. 5] 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 ..."
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Cited by 14 (11 self)
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The de Finetti Theorem is a cornerstone of the Bayesian approach. Bernardo [4, p. 5] 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 con…dence 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. We adopt multiplepriors utility as the benchmark model of preference and generalize the de Finetti Theorem to this framework. The resulting model also features a “conditionally IID ” representation, but it di¤ers from de Finetti in permitting the degree of con…dence in the evidence of symmetry to be subjective.
Lightning does not strike twice: Robust MDPs with coupled uncertainty
 In Proceedings of the 29th International Conference on Machine Learning (ICML12
, 2012
"... We consider Markov decision processes under parameter uncertainty. Previous studies all restrict to the case that uncertainties among different states are uncoupled, which leads to conservative solutions. In contrast, we introduce an intuitive concept, termed “Lightning Does not Strike Twice, ” to ..."
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Cited by 9 (1 self)
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We consider Markov decision processes under parameter uncertainty. Previous studies all restrict to the case that uncertainties among different states are uncoupled, which leads to conservative solutions. In contrast, we introduce an intuitive concept, termed “Lightning Does not Strike Twice, ” to model coupled uncertain parameters. Specifically, we require that the system can deviate from its nominal parameters only a bounded number of times. We give probabilistic guarantees indicating that this model represents real life situations and devise tractable algorithms for computing optimal control policies. 1.
Distributionally Robust Markov Decision Processes
"... We consider Markov decision processes where the values of the parameters are uncertain. This uncertainty is described by a sequence of nested sets (that is, each set contains the previous one), each of which corresponds to a probabilistic guarantee for a different confidence level so that a set of a ..."
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Cited by 7 (1 self)
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We consider Markov decision processes where the values of the parameters are uncertain. This uncertainty is described by a sequence of nested sets (that is, each set contains the previous one), each of which corresponds to a probabilistic guarantee for a different confidence level so that a set of admissible probability distributions of the unknown parameters is specified. This formulation models the case where the decision maker is aware of and wants to exploit some (yet imprecise) apriori information of the distribution of parameters, and arises naturally in practice where methods to estimate the confidence region of parameters abound. We propose a decision criterion based on distributional robustness: the optimal policy maximizes the expected total reward under the most adversarial probability distribution over realizations of the uncertain parameters that is admissible (i.e., it agrees with the apriori information). We show that finding the optimal distributionally robust policy can be reduced to a standard robust MDP where the parameters belong to a single uncertainty set, hence it can be computed in polynomial time under mild technical conditions. 1
2010, `The Ambiguity Premium vs. the Risk Premium under Limited Market Participation
"... This paper considers a stock market with ambiguityaverse informed investors under the CARAnormal setting, and studies the relationship between limited market participation and the equity premium which is decomposed into the risk premium and the ambiguity premium. In a rational expectations equili ..."
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Cited by 6 (0 self)
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This paper considers a stock market with ambiguityaverse informed investors under the CARAnormal setting, and studies the relationship between limited market participation and the equity premium which is decomposed into the risk premium and the ambiguity premium. In a rational expectations equilibrium, limited market participation arises if the largest deviation of investors ’ ambiguity increases sufficiently or if the variance of the stock return decreases sufficiently. In each case, a change in the risk premium and a change in the ambiguity premium may have opposite signs. This paper identifies conditions under which a change with the plus sign dominates and thus the equity premium increases when fewer investors participate in the stock market. JEL classication numbers: D81, D82, G12. Key words: asset price; ambiguity; asymmetric information; rational expectations. I am very grateful to the referee for many valuable comments. I thank Takao Asano, Hiroshi Fujiki,
Explicit reformulations of robust optimization problens with general uncertainty sets
 SIAM J. Optim
"... Abstract. We consider a rather general class of mathematical programming problems with data uncertainty, where the uncertainty set is represented by a system of convex inequalities. We prove that the robust counterparts of this class of problems can be equivalently reformulated as finite and explici ..."
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Cited by 5 (3 self)
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Abstract. We consider a rather general class of mathematical programming problems with data uncertainty, where the uncertainty set is represented by a system of convex inequalities. We prove that the robust counterparts of this class of problems can be equivalently reformulated as finite and explicit optimization problems. Moreover, we develop simplified reformulations for problems with uncertainty sets defined by convex homogeneous functions. Our results provide a unified treatment of many situations that have been investigated in the literature, and are applicable to a wider range of problems and more complicated uncertainty sets than those considered before. The analysis in this paper makes it possible to use existing continuous optimization algorithms to solve more complicated robust optimization problems. The analysis also shows how the structure of the resulting reformulation of the robust counterpart depends both on the structure of the original nominal optimization problem and on the structure of the uncertainty set. Key words. Robust optimization, data uncertainty, mathematical programming, homogeneous functions, convex analysis AMS subject classifications. 90C30, 90C15, 90C34, 90C25, 90C05.
AMBIGUITY AND AMBIGUITY AVERSION
, 2013
"... The phenomena of ambiguity and ambiguity aversion, introduced in Daniel Ellsberg’s seminal 1961 article, are ubiquitous in the realworld and violate both the key rationality axioms and classic models of choice under uncertainty. In particular, they violate the hypothesis that individuals’ uncertain ..."
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Cited by 4 (0 self)
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The phenomena of ambiguity and ambiguity aversion, introduced in Daniel Ellsberg’s seminal 1961 article, are ubiquitous in the realworld and violate both the key rationality axioms and classic models of choice under uncertainty. In particular, they violate the hypothesis that individuals’ uncertain beliefs can be represented by subjective probabilities (sometimes called personal probabilities or priors). This chapter begins with a review of early notions of subjective probability and Leonard Savage’s joint axiomatic formalization of expected utility and subjective probability. It goes on to describe Ellsberg’s classic urn paradoxes and the extensive experimental literature they have inspired. It continues with analytical descriptions of the numerous (primarily axiomatic) models of ambiguity aversion which have been developed by economic theorists, and concludes with a discussion of some current theoretical topics and newer