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Time-inconsistent stochastic linear-quadratic control problem with indefinite control weight costs

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Abstract

A time-inconsistent linear-quadratic optimal control problem for stochastic differential equations is studied. We introduce conditions where the control cost weighting matrix is possibly singular. Under such conditions, we obtain a family of closed-loop equilibrium strategies via multi-person differential games. This result extends Yong’s work (2017) in the case of stochastic differential equations, where a unique closed-loop equilibrium strategy can be derived under standard conditions (namely, the control cost weighting matrix is uniformly positive definite, and the other weighting coefficients are positive semidefinite).

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 12025105, 11971334 and 11931011), the Chang Jiang Scholars Program and the Science Development Project of Sichuan University (Grant Nos. 2020SCUNL101 and 2020SCUNL201).

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  1. School of Mathematics, Sichuan University, Chengdu, 610064, China

    Qi Lü & Bowen Ma

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  1. Qi Lü
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  2. Bowen Ma
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Correspondence to Qi Lü.

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Lü, Q., Ma, B. Time-inconsistent stochastic linear-quadratic control problem with indefinite control weight costs. Sci. China Math. 67, 211–236 (2024). https://doi.org/10.1007/s11425-022-2106-6

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  • DOI: https://doi.org/10.1007/s11425-022-2106-6

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