A Linear-quadratic Mean-Field Stochastic Stackelberg Differential Game with Random Exit Time

2021/04/28 by Zhun Gou, Gou, Zhun, Nan‐jing Huang +4
Economics, Econometrics and Finance · Mathematics · Medicine · #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Optimization and Control (math.OC) #Stochastic processes and financial applications #math.FA #math.OC

paper · pdf · doi:10.48550/arxiv.2104.13528

openalex publication_date 2021/04/28 · openalex created_date 2021/05/10 · arxiv created 2021/06/07 · arxiv updated 2021/06/08 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate a new model of a linear-quadratic mean-field stochastic Stackelberg differential game with one leader and two followers, in which the leader is allowed to stop her strategy at a random time. Our overarching goal is to find the Stackelberg solution of the leader and followers for such a model. By employing the backward induction method, the state equation is divided into two-stage equations. Moreover, by using the maximum principle and the verification theorem, the Stackelberg solution is obtained for such a model.

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