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

• Published in: Optimization Vol. 74; no. 4; pp. 981 - 1022
• Main Authors: Chen, Xin, Tian, Chenlei, Jin, Ting
• Format: Journal Article
• Language: English
• 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
• ISSN: 0233-1934; 1029-4945
• DOI: 10.1080/02331934.2023.2284968

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.