A paradox in time-consistency in the mean–variance problem?

Alain Bensoussan (), Kwok Chuen Wong () and Sheung Chi Phillip Yam ()
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Alain Bensoussan: The University of Texas at Dallas
Kwok Chuen Wong: Dublin City University
Sheung Chi Phillip Yam: Chinese University of Hong Kong

Finance and Stochastics, 2019, vol. 23, issue 1, No 5, 173-207

Abstract: Abstract We establish new conditions under which a constrained (no short-selling) time-consistent equilibrium strategy, starting at a certain time, will beat the unconstrained counterpart, as measured by the magnitude of their corresponding equilibrium mean–variance value functions. We further show that the pure strategy of solely investing in a risk-free bond can sometimes simultaneously dominate both constrained and unconstrained equilibrium strategies. With numerical experiments, we also illustrate that the constrained strategy can dominate the unconstrained one for most of the commencement dates (even more than 90%) of a prescribed planning horizon. Under a precommitment approach, the value function of an investor increases with the size of the admissible sets of strategies. However, this may fail to be true under the game-theoretic paradigm, as the constraint of time-consistency itself affects the value function differently when short-selling is and is not prohibited.

Keywords: Time-consistency; Mean–variance; State-dependent risk-aversion; Equilibrium strategy; Short-selling prohibition; 60J25; 91G10; 91G80 (search for similar items in EconPapers)
JEL-codes: C72 C73 G11 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s00780-018-00381-0

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