Time-Consistency of Optimal Investment under Smooth Ambiguity

35 Pages Posted: 22 Sep 2017 Last revised: 28 Feb 2019

See all articles by Anne Balter

Anne Balter

Tilburg University; Netspar

Antje Brigitte Mahayni

Mercator School of Management

Nikolaus Schweizer

Tilburg School of Economics and Management

Date Written: January 9, 2019

Abstract

We study portfolio choice in a Black-Scholes world under drift uncertainty. Preferences towards risk and ambiguity are modeled using the smooth ambiguity approach under a double power utility assumption and a normal distribution assumption on the unknown drift. Optimal investment in this setting is time-inconsistent: While utility is maximized by a precommitment strategy resembling the classical Merton solution, the investor’s future selves prefer to constantly increase the riskiness of the strategy. In contrast, the optimal dynamically consistent investment strategy accounts for variations in the perceived severity of drift uncertainty, thus increasing the riskiness of the strategy gradually over time. We provide a detailed comparative analysis of the mechanics and interplay of ambiguity, myopia and optimal decisions in this setting. We show that an investor who pre-commits will regret that decision from some time point onwards, wishing that she had followed the dynamically consistent strategy. This “point of regret” always lies near the middle of the investment horizon.

Keywords: Optimal Investment, Smooth Ambiguity, Ambiguity Aversion, Time-Consistency, Pre-Commitment

JEL Classification: G11, D81

Suggested Citation

Balter, Anne and Mahayni, Antje B. and Schweizer, Nikolaus, Time-Consistency of Optimal Investment under Smooth Ambiguity (January 9, 2019). Available at SSRN: https://ssrn.com/abstract=3040545 or http://dx.doi.org/10.2139/ssrn.3040545

Anne Balter (Contact Author)

Tilburg University ( email )

P.O. Box 90153
Tilburg, DC Noord-Brabant 5000 LE
Netherlands

Netspar ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Antje B. Mahayni

Mercator School of Management ( email )

Lotharstraße 65
Duisburg, Nordrhein-Westfalen 47057
Germany

Nikolaus Schweizer

Tilburg School of Economics and Management ( email )

PO Box 90153
Tilburg, 5000 LE Ti
Netherlands

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