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

• Main Authors: Han, Bingyan, Pun, Chi Seng, Wong, Hoi Ying
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2022
• Subjects: Science::Mathematics; Closed-Loop Control; State-Dependence
• Online Access: https://hdl.handle.net/10356/155833
• Institution: Nanyang Technological University

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.