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Article Dans Une Revue ESAIM: Control, Optimisation and Calculus of Variations Année : 2022

Constrained stochastic LQ control on infinite time horizon with regime switching

Résumé

This paper is concerned with a stochastic linear-quadratic (LQ) optimal control problem on infinite time horizon, with regime switching, random coefficients, and cone control constraint. To tackle the problem, two new extended stochastic Riccati equations (ESREs) on infinite time horizon are introduced. The existence of the nonnegative solutions, in both standard and singular cases, is proved through a sequence of ESREs on finite time horizon. Based on this result and some approximation techniques, we obtain the optimal state feedback control and optimal value for the stochastic LQ problem explicitly. Finally, we apply these results to solve a lifetime portfolio selection problem of tracking a given wealth level with regime switching and portfolio constraint.

Dates et versions

hal-03540461 , version 1 (24-01-2022)

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Citer

Ying Hu, Xiaomin Shi, Zuo Quan Xu. Constrained stochastic LQ control on infinite time horizon with regime switching. ESAIM: Control, Optimisation and Calculus of Variations, 2022, 28, pp.5. ⟨10.1051/cocv/2021110⟩. ⟨hal-03540461⟩
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