Optimal control and zero-sum game subject to multifactor uncertain random systems with jump

A differential equation incorporating random matrices, multiple Liu processes, and multiple V jump processes is employed to portray a multifactor uncertain random system with jump. The existence and uniqueness theorem for such an equation is proved. Based on the theorem, problems of optimal control...

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Bibliographic Details
Published inOptimization Vol. 74; no. 4; pp. 981 - 1022
Main Authors Chen, Xin, Tian, Chenlei, Jin, Ting
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 12.03.2025
Taylor & Francis LLC
Subjects
Differential equations
Equilibrium equations
Existence theorems
Game theory
Games
Liu process
Optimal control
Optimization
Problem solving
Saddle points
saddle-point
Uncertain random system
Uniqueness theorems
V jump process
Zero sum games
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Summary:A differential equation incorporating random matrices, multiple Liu processes, and multiple V jump processes is employed to portray a multifactor uncertain random system with jump. The existence and uniqueness theorem for such an equation is proved. Based on the theorem, problems of optimal control and two-person zero-sum game subject to multifactor uncertain random systems with jump are considered. An equation of optimality is provided for solving a problem of optimal control. Equilibrium equations are proposed to identify the saddle-point of a two-person zero-sum game problem. As an extension, we generalize the obtained results to the problems subject to differential equations including random matrices, multiple Liu processes, and multiple V-n jumps processes. Finally, a portfolio selection game problem is analysed utilizing the acquired theoretical results.
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2023.2284968