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arXiv · 2312.08713

Time-inconsistent Linear Quadratic Optimal Control Problem for Forward-Backward Stochastic Differential Equations

Qi Lü·Bowen Ma
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Abstract

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 closed-loop 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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Qi Lü, Bowen Ma. 2023-12-14. Time-inconsistent Linear Quadratic Optimal Control Problem for Forward-Backward Stochastic Differential Equations. https://arxiv.org/abs/2312.08713

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