论文标题
线性季度随机stackelberg差异游戏用于跳跃系统
Linear-Quadratic Stochastic Stackelberg Differential Games for Jump-Diffusion Systems
论文作者
论文摘要
本文考虑了线性季度（LQ）随机领导者Stackelberg差异游戏，用于具有随机系数的跳跃扩散系统。我们首先使用随机最大原理解决了追随者的LQ问题，并根据插座式Riccati微分方程（ISRDE）获得了开环最佳解决方案的状态反馈表示，其中通过Squares方法完成了状态回馈类型控制。接下来，我们使用变分方法为领导者的无限LQ随机最佳控制问题建立了随机最大原理。但是，为了获得针对领导者的开环解决方案的状态反馈表示，由于跳跃过程存在技术挑战。为了克服这一限制，我们考虑了两种不同的情况，在这种情况下，可以通过概括四步方案来表征对ISRDE的国家反馈类型最佳控制。最后，在这两种情况下，我们表明了针对领导者和追随者的开环最佳解决方案的状态反馈表示形式构成了Stackelberg平衡。请注意，由于追随者的合理行为引起的耦合的FBSDE约束，领导者的（不确定）LQ控制问题是新的和非平地的。
This paper considers linear-quadratic (LQ) stochastic leader-follower Stackelberg differential games for jump-diffusion systems with random coefficients. We first solve the LQ problem of the follower using the stochastic maximum principle and obtain the state-feedback representation of the open-loop optimal solution in terms of the integro-stochastic Riccati differential equation (ISRDE), where the state-feedback type control is shown to be optimal via the completion of squares method. Next, we establish the stochastic maximum principle for the indefinite LQ stochastic optimal control problem of the leader using the variational method. However, to obtain the state-feedback representation of the open-loop solution for the leader, there is a technical challenge due to the jump process. To overcome this limitation, we consider two different cases, in which the state-feedback type optimal control for the leader in terms of the ISRDE can be characterized by generalizing the Four-Step Scheme. Finally, in these two cases, we show that the state-feedback representation of the open-loop optimal solutions for the leader and the follower constitutes the Stackelberg equilibrium. Note that the (indefinite) LQ control problem of the leader is new and nontrivial due to the coupled FBSDE constraint induced by the rational behavior of the follower.
