A Linear Quadratic Stochastic Stackelberg Differential Game with Time Delay

2020/12/28 by Weijun Meng, Meng, Weijun, Jingtao Shi +1
Economics, Econometrics and Finance · Medicine · Physics and Astronomy · #34K35 #34K50 #49N10 #60H10 #91A15 #91A65 #93E20 #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Optimization and Control (math.OC) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2012.14145

openalex publication_date 2020/12/28 · openalex created_date 2021/01/05 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with a linear quadratic stochastic Stackelberg differential game with time delay. The model is general, in which the state delay and the control delay both appear in the state equation, moreover, they both enter into the diffusion term. By introducing two Pseudo-Riccati equations and a special matrix equation, the state feedback representation of the open-loop Stackelberg strategy is derived, under some assumptions. Finally, two examples are given to illustrate the applications of the theoretical results.

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