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

31 Pages Posted: 8 Jan 2019 Last revised: 2 Jul 2021

See all articles by Bingyan Han

Bingyan Han

Division of Science and Technology, BNU-HKBU United International College

Chi Seng Pun

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences

Hoi Ying Wong

The Chinese University of Hong Kong (CUHK) - Department of Statistics

Date Written: June 10, 2021

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

JEL Classification: C72, C73, D81, G11

Suggested Citation

Han, Bingyan and Pun, Chi Seng and Wong, Hoi Ying, Robust state-dependent mean-variance portfolio selection: a closed-loop approach (June 10, 2021). Available at SSRN: https://ssrn.com/abstract=3306305 or http://dx.doi.org/10.2139/ssrn.3306305

Bingyan Han

Division of Science and Technology, BNU-HKBU United International College ( email )

Zhuhai
China

HOME PAGE: http://https://sites.google.com/site/hanbyan/home

Chi Seng Pun (Contact Author)

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences ( email )

SPMS-MAS-05-22
21 Nanyang Link
Singapore, 637371
Singapore
(+65) 6513 7468 (Phone)

HOME PAGE: http://personal.ntu.edu.sg/cspun/

Hoi Ying Wong

The Chinese University of Hong Kong (CUHK) - Department of Statistics ( email )

Shatin, N.T.
Hong Kong

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