Non-homogeneous stochastic linear-quadratic optimal control problems with multidimensional state and regime switching

Abstract

In this paper, we explore non-homogeneous stochastic linear-quadratic (LQ) optimal control problems with multidimensional states and regime switching. We focus on the corresponding stochastic Riccati equation (SRE), which mirrors that of the homogeneous stochastic LQ optimal control problem, and the adjoint backward stochastic differential equation (BSDE), which arises from the non-homogeneous terms in the state equation and cost functional. We solve both the SRE and adjoint BSDE using the contraction mapping method, which helps represent the closed-loop optimal control and the optimal value of our problems. In particular, we extend some results of Hu et al. [7] to the multidimensional case.

Keywords

Non-homogeneous stochastic LQ problem / Regime switching / Multidimensional state / BSDE / Unbounded coefficients

Acknowledgements

Financial support from the National Natural Science Foundation of China (Grant Nos. 12101400 and 12326603) is gratefully acknowledged. The authors would like to thank the editor and reviewer for their valuable comments and suggestions.

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