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Robust state-dependent mean–variance portfolio selection: a closed-loop approach

Bingyan Han (), Chi Seng Pun () and Hoi Ying Wong ()
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Bingyan Han: BNU-HKBU United International College
Chi Seng Pun: Nanyang Technological University
Hoi Ying Wong: The Chinese University of Hong Kong

Finance and Stochastics, 2021, vol. 25, issue 3, No 4, 529-561

Abstract: Abstract This paper studies a class of robust mean–variance portfolio selection problems with state-dependent risk aversion. Model uncertainty, in the sense of considering alternative dominated models, is introduced to the problem to reflect the investor’s uncertainty-averse preference. To characterise the robust portfolios, we consider closed-loop equilibrium control and spike variation approaches. Moreover, we show that a closed-loop equilibrium strategy exists and is unique under some technical conditions. This partially addresses open problems left in Björk et al. (Finance Stoch. 21:331–360, 2017) and Pun (Automatica 94:249–257, 2018). By using a necessary and sufficient condition for the equilibrium, we manage to derive the analytical form of the equilibrium strategy via the unique solution to a nonlinear ordinary differential equation system. To validate the proposed closed-loop control framework, we show that when there is no uncertainty, our equilibrium strategy is reduced to the strategy in Björk et al. (Math. Finance 24:1–24, 2014), which cannot be deduced under the open-loop control framework.

Keywords: Closed-loop control; Robust mean–variance portfolio selection; State-dependence; Time-inconsistency; Model uncertainty; 49N90; 91A80; 91G10; 91G80 (search for similar items in EconPapers)
JEL-codes: C72 C73 D81 G11 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00780-021-00457-4

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