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

Lü, Qi; Ma, Bowen

doi:10.1007/s11425-022-2106-6

Sci. China Math.

2023

DOI: 10.1007/s11425-022-2106-6

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

Qi Lü,

Bowen Ma

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2024

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Time-inconsistent linear quadratic optimal control problem for forward–backward stochastic differential equations

Lü,

2024

ESAIM: COCV

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We study the time-inconsistent linear quadratic optimal control problem for forward–backward stochastic differential equations with potentially indefinite cost weighting matrices for both the state and the control variables. Our research makes two contributions. Firstly, we introduce a novel type of Riccati equation system with parameters and constraint conditions, known as the generalized equilibrium Riccati equation. This equation system offers a comprehensive solution for the closedloop equilibrium strategy of the problem at hand. Secondly, we establish the well-posedness of the generalized equilibrium Riccati equation for the one-dimensional case, provided certain conditions are met.

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Time-inconsistent linear quadratic optimal control problem for forward–backward stochastic differential equations

Lü,

2024

ESAIM: COCV

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

Cited by 1 publication

References 26 publications

Time-inconsistent linear quadratic optimal control problem for forward–backward stochastic differential equations

Time-inconsistent linear quadratic optimal control problem for forward–backward stochastic differential equations

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