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Time-Consistent Strategies for Multi-Period Portfolio Optimization with/without the Risk-Free Asset

Zhou, Zhongbao, Liu, Xianghui, Xiao, Helu, Ren, TianTian, Liu, Wenbin (2018) Time-Consistent Strategies for Multi-Period Portfolio Optimization with/without the Risk-Free Asset. Mathematical Problems in Engineering, 2018 . ISSN 1024-123X. (doi:10.1155/2018/7563093) (KAR id:69515)

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Abstract

The pre-commitment and time-consistent strategies are the two most representative investment strategies for the classic multi-period mean-variance portfolio selection problem. In this paper, we revisit the case in which there exists one risk-free asset in the market and prove that the time-consistent solution is equivalent to the optimal open-loop solution for the classic multi-period mean-variance model. Then, we further derive the explicit time-consistent solution for the classic multi-period mean-variance model only with risky assets, by constructing a novel Lagrange function and using backward induction. Also, we prove that the Sharpe ratio with both risky and risk-free assets strictly dominates that of only with risky assets under the time-consistent strategy setting. After the theoretical investigation, we perform extensive numerical simulations and out-of-sample tests to compare the performance of pre-commitment and time-consistent strategies. The empirical studies shed light on the important question: what is the primary motivation of using the time-consistent investment strategy.

Item Type: Article
DOI/Identification number: 10.1155/2018/7563093
Subjects: Q Science > QA Mathematics (inc Computing science) > QA 76 Software, computer programming,
Divisions: Faculties > Social Sciences > Kent Business School > Management Science
Depositing User: Steve Liu
Date Deposited: 11 Oct 2018 08:53 UTC
Last Modified: 06 May 2020 03:18 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/69515 (The current URI for this page, for reference purposes)
Liu, Wenbin: https://orcid.org/0000-0001-5966-6235
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