# American Institute of Mathematical Sciences

July  2019, 15(3): 1493-1515. doi: 10.3934/jimo.2018106

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

 1 School of Business Administration, Hunan University, Changsha 410082, China 2 Business School, Hunan Normal University, Changsha 410081, China 3 Business School, University of Kent, Kent, CT2 7PE, UK

* Corresponding author: Zhongbao Zhou

Received  January 2018 Revised  March 2018 Published  July 2018

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.

Citation: Zhongbao Zhou, Ximei Zeng, Helu Xiao, Tiantian Ren, Wenbin Liu. Multiperiod portfolio optimization for asset-liability management with quadratic transaction costs. Journal of Industrial & Management Optimization, 2019, 15 (3) : 1493-1515. doi: 10.3934/jimo.2018106
##### References:

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##### References:
The M-V frontiers under different strategies with/without cost
The M-V frontiers under different strategies
The efficient frontiers of strategies under different costaversion coefficient
The efficient frontiers of strategies under different parameter
The parameter set
 $\Lambda^1$ $\Lambda^2$ $\Lambda^3$ $\Lambda^4$ $0.001 *\begin{bmatrix} 1& 0 & 0 \\ 0 & 1& 0 \\ 0 & 0 & 1 \end{bmatrix}$ $0.001*\begin{bmatrix} 3& 0 & 0 \\ 0 & 1& 0 \\ 0 & 0 & 1 \end{bmatrix}$ $0.001*\begin{bmatrix} 1& 0 & 0 \\ 0 & 3& 0 \\ 0 & 0 & 1 \end{bmatrix}$ $0.001*\begin{bmatrix} 1& 0 & 0 \\ 0 & 1& 0 \\ 0 & 0 & 3 \end{bmatrix}$
 $\Lambda^1$ $\Lambda^2$ $\Lambda^3$ $\Lambda^4$ $0.001 *\begin{bmatrix} 1& 0 & 0 \\ 0 & 1& 0 \\ 0 & 0 & 1 \end{bmatrix}$ $0.001*\begin{bmatrix} 3& 0 & 0 \\ 0 & 1& 0 \\ 0 & 0 & 1 \end{bmatrix}$ $0.001*\begin{bmatrix} 1& 0 & 0 \\ 0 & 3& 0 \\ 0 & 0 & 1 \end{bmatrix}$ $0.001*\begin{bmatrix} 1& 0 & 0 \\ 0 & 1& 0 \\ 0 & 0 & 3 \end{bmatrix}$
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