Abstract
This paper considers an equilibrium asset pricing model in a static pure exchange economy under ambiguity. Ambiguity preference is represented by the dual theory of the smooth ambiguity model [6]. 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.
Highlights
The state price density (SPD) is a central concept in modern asset pricing theory.1 Given the SPD and its probability distribution, we can price every asset.it is essential to derive the SPD for asset pricing
Using the SPD, we extend the classical capital asset pricing model (CAPM) to an economy under ambiguity
This paper studies an equilibrium asset pricing model for a static pure exchange economy with ambiguity
Summary
The state price density (SPD) is a central concept in modern asset pricing theory. Given the SPD and its probability distribution, we can price every asset. As shown in [6], an equivalent representation of the dual theory is the “single” expected utility with respect to a mixture of the first-order probability distributions with the distorted 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. Ambiguity preference does not explicitly appear for most of the main analysis While this tractability is a distinct advantage compared with existing models, ambiguity preferences have an effect on equilibria in securities markets. We clarify these effects through comparative statics of the SPD.
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