T u f s, t dq t d p s where p is a probability measure over first-stage events ESq is a probability measure over second-stage events ETu: They are a special case of variational preferences, seen by taking c that is zero on C and infinite outside of C.
Ambiguity preference is represented by the dual theory of the smooth ambiguity model . We show the existence and the uniqueness of the equilibrium in the economy and derive the state price density SPD. The equilibrium excess return, which can be seen as an extension of the capital asset pricing model CAPM under risk to ambiguity, is derived from the SPD.
We also determine the effects of ambiguity preference on the excess returns of ambiguous securities through comparative statics of the SPD. Introduction The state price density SPD is a central concept in modern asset pricing theory.
Thus, it is essential to derive the SPD for asset pricing. A lot of studies have attempted to derive the SPD from both a theoretical and an empirical viewpoint. Most asset pricing models suppose that an agent can assign a unique probability distribution over a state space.
However, it is commonly observed that such a unique probability is not available in the economy. It is known that expected utility, which is a dominant tool in asset pricing theory, cannot describe choice under ambiguity.
Following  , ambiguity is represented by a second-order probability over the set of first-order probabilities over the state space in this paper. This paper unites the above two lines of research. The purpose of this paper is to characterize the SPD in the presence of ambiguity.
More precisely, we examine equilibrium in a single-period pure exchange economy under ambiguity and derive the SPD by using the dual theory of the smooth ambiguity model .
We also derive the equilibrium excess return using the SPD, which can be viewed as an extension of the classical capital asset pricing model CAPM  . The tractability of this model is a distinct advantage compared with other existing ambiguity models. The ambiguity preference is reflected by the shape of the transformation.
Unlike the original theory, the dual theory of the smooth ambiguity model by  captures ambiguity preference by a distortion of the second-order probability distribution.
This form reinforces the advantage of the original theory that the existing results in the expected utility are applicable to decision problems under ambiguity, while maintaining descriptive validity for ambiguity.
This advantage makes it easy to characterize equilibria under ambiguity compared with the original theory as shown later in this paper. Thus the dual theory might be a powerful tool for these kinds of analyses.
A series of studies on equilibrium analysis in securities markets precede this paper. This paper derives the SPD in an economy with a representative agent. For the construction of the representative agent, we use the idea of assigning proper weights to each agent, which goes back to .
This paper also shows the existence and the uniqueness of the equilibrium in an economy. We adapt the dual method of   to show the existence and the uniqueness of the equilibrium in an economy. Thus, this paper is related to the recent literature on the CAPM under ambiguity.
In particular,  and  considered the CAPM under ambiguity using the smooth ambiguity model. Even though these papers derive a similar form of the excess return in the CAPM, it should be noted that we do not require any approximations to derive the CAPM, whereas  and  used a quadratic approximation.
Furthermore, the optimal portfolio for each agent can be shown to consist of his specific portfolio in addition to a safe security and the market portfolio. Because we adopt the dual theory of the smooth ambiguity model by , ambiguity preference is embedded in the expected utility representation with a distorted probability.
In other words, ambiguity preference does not explicitly appear for most of the main analysis.Abstract.
This article characterizes a family of preference relations over uncertain prospects that (a) are dynamically consistent in the Machina sense and, moreover, for which the updated preferences are also members of this family and (b) can simultaneously accommodate Ellsberg- and Allais-type paradoxes.
tion: the winning candidate’s platform is generally overly ambiguous. While our theory rationalizes a positive correlation between ambiguity and electoral success, it shows that voters’ risk preferences (Zeckhauser,;Shepsle,;Aragones and Postlewaite,) or tailor policy to an initially-uncertain “state of the world.
and techniques for analyzing risk and risk preferences to an investigation of ambiguity and ambiguity preferences. The model is used by Snow (, ) to show that greater ambiguity aversion.
We review evidence, recent theoretical explanations, and applications of research on ambiguity and SEU. ambiguity decision-making preference survey uncertainty utility-theory Search all the public and authenticated articles in CiteULike.
Risk, ambiguity, and state-preference theory imprecision of beliefs. The preferences of such a decision maker do have an indif-ference curve representation, which . Preference, belief, and similarity:selected writings/by Amos Tversky;edited by Eldar Shaﬁr.
Choice under Risk and Uncertainty 22 Prospect Theory: An Analysis of Decision under Risk Daniel Kahneman and Amos Tversky 26 Preference and Belief: Ambiguity and Competence in Choice under Uncertainty Chip Heath and Amos Tversky.