Optimal Control for a Multistage Uncertain Random System

Chen, Xin; Jin, Ting

doi:10.1109/access.2023.3234068

Cited by 4 publications

(2 citation statements)

References 34 publications

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“…Define Nash equilibrium of linear quadratic jump uncertain stochastic differential game problems [5]- [7] as follows Definition 1: ( [28], [29]) If the admissible control pair…”

Section: Linear Quadratic Jump Uncertainty Stochastic Non-zero-sum Di...mentioning

confidence: 99%

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Research on Enterprise Investment Decision Based on Linear Quadratic Jump Uncertainty Stochastic Differential Game

Yang,

Zhang,

Wang

et al. 2024

IEEE Access

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Aiming at the objective uncertainty, subjective uncertainty, and extreme events may be in a dynamic system simultaneously. This paper focuses on the differential game problem of a linear quadratic jump uncertain stochastic system. The system is described by both a jump uncertain differential equation and a stochastic differential equation. The principle of optimality and equation of optimality are established. Then, a differential game model based on linear quadratic jump uncertain stochastic system is constructed. Furthermore, Nash equilibrium are discussed by using the obtained equation. Finally, its application in the dynamic investment decision of enterprises is given, and numerical simulations are performed. This approach offers a new method for quantitative analysis in future studies.

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“…Define Nash equilibrium of linear quadratic jump uncertain stochastic differential game problems [5]- [7] as follows Definition 1: ( [28], [29]) If the admissible control pair…”

Section: Linear Quadratic Jump Uncertainty Stochastic Non-zero-sum Di...mentioning

confidence: 99%

“…There are limited studies focusing on uncertain stochastic optimal control problems and jump uncertain stochastic optimal control problems. For instance, Chen and Jin [5] researched the optimal control of a multistage uncertain random system. Chen et al [6] also studied the optimal control problem of jump uncertain stochastic dynamic systems.…”

mentioning

confidence: 99%

Research on Enterprise Investment Decision Based on Linear Quadratic Jump Uncertainty Stochastic Differential Game

Yang,

Zhang,

Wang

et al. 2024

IEEE Access

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Optimal control problems subject to uncertain random discrete-time noncausal systems

Chen

Yuan

et al. 2023

Chaos, Solitons & Fractals

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Dynamic programming principle for optimal control of uncertain random differential equations and its application to optimal portfolio selection

Chirima,

Matenda,

Chikodza

et al. 2024

RoBES

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This study aimed to examine an uncertain stochastic optimal control problem premised on an uncertain stochastic process. The proposed approach is used to solve an optimal portfolio selection problem. This paper’s research is relevant because it outlines the procedure for solving optimal control problems in uncertain random environments. We implement Bellman’s principle of optimality method in dynamic programming to derive the principle of optimality. Then the resulting Hamilton-Jacobi-Bellman equation (the equation of optimality in uncertain stochastic optimal control) is used to solve a proposed portfolio selection problem. The results of this study show that the dynamic programming principle for optimal control of uncertain stochastic differential equations can be applied in optimal portfolio selection. Also, the study results indicate that the optimal fraction of investment is independent of wealth. The main conclusion of this study is that, in Itô-Liu financial markets, the dynamic programming principle for optimal control of uncertain stochastic differential equations can be applied in solving the optimal portfolio selection problem.

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Optimal Control for a Multistage Uncertain Random System

Cited by 4 publications

References 34 publications

Research on Enterprise Investment Decision Based on Linear Quadratic Jump Uncertainty Stochastic Differential Game

Research on Enterprise Investment Decision Based on Linear Quadratic Jump Uncertainty Stochastic Differential Game

Optimal control problems subject to uncertain random discrete-time noncausal systems

Dynamic programming principle for optimal control of uncertain random differential equations and its application to optimal portfolio selection

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