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Optimal Control of Constrained Stochastic Linear-Quadratic Model with Applications

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  • Weiping Wu
  • Jianjun Gao
  • Junguo Lu
  • Xun Li

Abstract

This paper studies a class of continuous-time scalar-state stochastic Linear-Quadratic (LQ) optimal control problem with the linear control constraints. Applying the state separation theorem induced from its special structure, we develop the explicit solution for this class of problem. The revealed optimal control policy is a piece-wise affine function of system state. This control policy can be computed efficiently by solving two Riccati equations off-line. Under some mild conditions, the stationary optimal control policy can be also derived for this class of problem with infinite horizon. This result can be used to solve the constrained dynamic mean-variance portfolio selection problem. Examples shed light on the solution procedure of implementing our method.

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  • Weiping Wu & Jianjun Gao & Junguo Lu & Xun Li, 2018. "Optimal Control of Constrained Stochastic Linear-Quadratic Model with Applications," Papers 1806.03624, arXiv.org.
    • Handle: RePEc:arx:papers:1806.03624
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    References listed on IDEAS

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    1. Xiangyu Cui & Duan Li & Xun Li, 2017. "Mean-Variance Policy For Discrete-Time Cone-Constrained Markets: Time Consistency In Efficiency And The Minimum-Variance Signed Supermartingale Measure," Mathematical Finance, Wiley Blackwell, vol. 27(2), pages 471-504, April.
    2. Duan Li & Wan‐Lung Ng, 2000. "Optimal Dynamic Portfolio Selection: Multiperiod Mean‐Variance Formulation," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 387-406, July.
    3. Cui, Xiangyu & Gao, Jianjun & Li, Xun & Li, Duan, 2014. "Optimal multi-period mean–variance policy under no-shorting constraint," European Journal of Operational Research, Elsevier, vol. 234(2), pages 459-468.
    4. Weipin Wu & Jianjun Gao & Duan Li & Yun Shi, 2017. "Explicit Solution for Constrained Stochastic Linear-Quadratic Control with Multiplicative Noise," Papers 1709.05529, arXiv.org.
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