Multiperiod portfolio optimization for asset-liability management with quadratic transaction costs

Zhongbao Zhou,,School Of Business Administration, Hunan University, Changsha 410082, China ,Wenbin Liu,Ximei Zeng,Tiantian Ren,Helu Xiao,,Business School, University Of Kent, Kent, Ct2 7Pe, Uk ,,Business School, Hunan Normal University, Changsha 410081, China

doi:10.3934/jimo.2018106

Zhongbao Zhou, ,School Of Business Administration, Hunan University, Changsha 410082, China + Show 6 more

Open Access

https://doi.org/10.3934/jimo.2018106

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Abstract

This paper investigates the multiperiod asset-liability management problem with quadratic transaction costs. Under the mean-variance criteria, we construct tractability models with/without the riskless asset and obtain the pre-commitment and time-consistent investment strategies through the application of embedding scheme and backward induction approach, respectively. In addition, some conclusions in the existing literatures can be regarded as the degenerated cases under our setting. Finally, the numerical simulations are given to show the difference of frontiers derived by different strategies. Also, some interesting findings on the impact of quadratic transaction cost parameters on efficient frontiers are discussed.

Highlights

Asset-liability management (ALM) is a general risk management problem for financial services companies, such as pension funds and insurance companies
ALM involves the management of assets in such a way as to earn adequate returns while maintaining a comfortable surplus of assets over existing and future liabilities
The mean-variance asset-liability management (MVALM) problem is a portfolio optimization problem, so as to realize the trade-off between the expectation of the terminal surplus maximization and minimum risk measured by the variance of the terminal surplus

Summary

Introduction

Asset-liability management (ALM) is a general risk management problem for financial services companies, such as pension funds and insurance companies. This approach is limited to one or two investment stages, and the investor can only invest one riskless asset and one risky asset To deal with this dilemma, Gârleanu and Pedersen (2013) promoted the optimal feedback solution for dynamic portfolios with a quadratic transaction cost which was followed by some researchers, such as Boyd et al (2014), DeMiguel et al (2015) and Zhang et al (2017). Motivated by the difficulties for multiperiod asset-liability management problem with transaction costs, we provide the tractability framework to obtain the analytic solutions, which considers the quadratic transaction costs adopted by Gârleanu and Pedersen (2013). Let v(t) { vt , vt 1,..., vT 1} be the strategy at period t , and the multiperiod asset-liability management problem with quadratic transaction costs can be expressed as: Ft ( J t , v(t )).

Analytical solutions of multiperiod MVALM problem with a riskless asset

Numerical simulations

Conclusion