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

  • * Corresponding author: Zhongbao Zhou

    * Corresponding author: Zhongbao Zhou 
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  • 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.

    Mathematics Subject Classification: Primary: 90C25; Secondary: 91G10.


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  • Figure 1.  The M-V frontiers under different strategies with/without cost

    Figure 2.  The M-V frontiers under different strategies

    Figure 3.  The efficient frontiers of strategies under different costaversion coefficient

    Figure 4.  The efficient frontiers of strategies under different parameter

    Table 1.  The parameter set

    $\Lambda^1$ $\Lambda^2$ $\Lambda^3$ $\Lambda^4$
    $0.001 *\begin{bmatrix} 1& 0 & 0 \\ 0 & 1& 0 \\ 0 & 0 & 1 \end{bmatrix}$ $0.001*\begin{bmatrix} 3& 0 & 0 \\ 0 & 1& 0 \\ 0 & 0 & 1 \end{bmatrix}$ $0.001*\begin{bmatrix} 1& 0 & 0 \\ 0 & 3& 0 \\ 0 & 0 & 1 \end{bmatrix}$ $0.001*\begin{bmatrix} 1& 0 & 0 \\ 0 & 1& 0 \\ 0 & 0 & 3 \end{bmatrix}$
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