Optimal Stock Investment under Ambiguity about Ambiguity

19 Pages Posted: 5 Feb 2020

See all articles by Dmitry Makarov

Dmitry Makarov

ICEF, Higher School of Economics

Date Written: January 28, 2020


A prominent approach to modelling ambiguity about the distribution of stock returns is to assume that this distribution is itself random and distributed according to a certain second-order distribution. Realistically, the second-order distribution can also be ambiguous implying ambiguity about ambiguity, a long-debated idea dating back to classical works by Hume (1738), Reichenbach (1949) and Savage (1954). Unlike extensive research into ambiguity, we are yet to understand how ambiguity about ambiguity affects investor behavior. Our paper makes a first step in this direction. We consider a setting with a bond and a risky stock whose expected return is ambiguous. Our key novelty is that both the mean and the variance of the associated second-order distribution are also ambiguous. We derive analytically the investor’s optimal stock investment and examine its properties.

Keywords: ambiguity about ambiguity, portfolio choice, higher-level probabilities, smooth ambiguity

JEL Classification: D81, G11, G41

Suggested Citation

Makarov, Dmitry, Optimal Stock Investment under Ambiguity about Ambiguity (January 28, 2020). Available at SSRN: https://ssrn.com/abstract=3526898 or http://dx.doi.org/10.2139/ssrn.3526898

Dmitry Makarov (Contact Author)

ICEF, Higher School of Economics ( email )

26 Shabolovka

HOME PAGE: http://www.nes.ru/~dmakarov

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