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Linear quadratic open-loop Stackelberg game for stochastic systems with Poisson jumps
Journal of the Franklin Institute ( IF 4.1 ) Pub Date : 2021-05-05 , DOI: 10.1016/j.jfranklin.2021.04.048
Yaning Lin

This paper is concerned with the finite horizon linear quadratic (LQ) Stackelberg game for stochastic systems with Poisson jumps under the open-loop information structure. First, the follower solves a LQ stochastic optimal control problem with Poisson jumps. With the aid of an introduced generalized differential Riccati equation with Poisson jumps (GDREP), the sufficient conditions for the optimization of the follower are put forward. Then, the leader faces an optimal control problem for a forward-backward stochastic differential equation with Poisson jumps (FBSDEP). By introducing new state and costate variables, a sufficient condition for the existence and uniqueness of the open-loop Stackelberg strategies is presented in terms of the solvability of two differential Riccati equations and a convexity condition. In addition, the state feedback representation of the open-loop Stackelberg strategies is obtained via the related differential Riccati equation. Finally, two examples shed light on the effectiveness of the obtained results.



中文翻译:

具有泊松跳跃的随机系统的线性二次开环 Stackelberg 博弈

本文关注的是在开环信息结构下具有泊松跳跃的随机系统的有限视界线性二次 (LQ) Stackelberg 博弈。首先,跟随者用泊松跳跃解决 LQ 随机最优控制问题。借助引入的具有泊松跳跃的广义微分Riccati方程(GDREP),提出了优化跟随器的充分条件。然后,领导者面临具有泊松跳跃的前向后向随机微分方程 (FBSDEP) 的最优控制问题。通过引入新的状态变量和协变量,根据两个微分 Riccati 方程的可解性和凸性条件,提出了开环 Stackelberg 策略的存在性和唯一性的充分条件。此外,开环 Stackelberg 策略的状态反馈表示是通过相关的微分 Riccati 方程获得的。最后,两个例子阐明了所得结果的有效性。

更新日期:2021-06-13
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