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

Abstract

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.