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arXiv · 2104.04747

Indefinite Backward Stochastic Linear-Quadratic Optimal Control Problems

Jingrui Sun·Zhen Wu·Jie Xiong
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Abstract

This paper is concerned with a backward stochastic linear-quadratic (LQ, for short) optimal control problem with deterministic coefficients. The weighting matrices are allowed to be indefinite, and cross-product terms in the control and state processes are present in the cost functional. Based on a Hilbert space method, necessary and sufficient conditions are derived for the solvability of the problem, and a general approach for constructing optimal controls is developed. The crucial step in this construction is to establish the solvability of a Riccati-type equation, which is accomplished under a fairly weak condition by investigating the connection with forward stochastic LQ optimal control problems.

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Jingrui Sun, Zhen Wu, Jie Xiong. 2021-04-10. Indefinite Backward Stochastic Linear-Quadratic Optimal Control Problems. https://arxiv.org/abs/2104.04747

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