Fat-tailed Distribution under the Smooth Ambiguity Model

Prince Osei
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Prince Osei: Center for Mathematical Economics, Bielefeld University

No 764, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

Abstract: We study the ambiguity-adjusted return distribution induced by an investor with smooth ambiguity preferences à la Klibanoff et al. (2005), who faces uncertainty about the variance of asset returns. The variance uncertainty is modeled using a gamma distribution, a second-order prior over the family of normally distributed returns. Our main results present a density distortion that exponentially tilts this prior into an ambiguity-adjusted gamma distribution, characterized by its distorted rate parameter and shape parameter. A smaller distorted rate parameter implies greater weight on high-variance returns. This paper derives the ambiguity-adjusted return distribution as a symmetric variance–gamma distribution reflecting the investor’s risk and ambiguity aversion. The ambiguity-averse investor assigns a variance–gamma distribution with a higher likelihood of extreme returns, while the ambiguity-neutral investor assigns a distribution more peaked around the mean. We obtain the ambiguity-adjusted return variance as an increasing function of risk and ambiguity aversion. An empirical comparison is performed to calibrate the ambiguity aversion parameter of an in- vestor investing in gold.

Keywords: sset returns; Smooth ambiguity aversion; Variance uncertainty; Variance– Gamma distribution (search for similar items in EconPapers)
Pages: 19
Date: 2026-02-11
New Economics Papers: this item is included in nep-upt
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