Linear-Quadratic Delayed Mean-Field Social Optimization
Linear-Quadratic Delayed Mean-Field Social Optimization
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DOI：
10.1007/s00245-023-10067-5
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发表时间：
2023-01
影响因子：
1.8
通讯作者：
Tianyang Nie;Shujun Wang;Zhanghua Wu
中科院分区：
文献类型：
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作者：
Tianyang Nie;Shujun Wang;Zhanghua Wu
研究了具有弱耦合大种群的线性二次(LQ)随机时滞优化问题。与经典的平均场(MF)博弈不同的是，在这里，主体之间相互合作，以最小化所谓的社会目标。借助于时滞逐人最优原理，得到分散信息的辅助LQ时滞控制问题。利用MF型期望正倒向随机时滞方程(AFBSDDE)相容条件，得到了一种分散策略。采用带延迟特征的贴现方法求解相容条件系统。最后，通过对AFBSDDEs的一些估计，我们得到了渐近的社会最优性。
A linear quadratic (LQ) stochastic optimization problem with delay involving weakly-coupled large population is investigated in this paper. Different to classic mean field (MF) game, here agents cooperate with each other to minimize the so-calledsocialobjective. With the aid ofdelayed person-by-person optimalityprinciple, one arrives at an auxiliary LQ delayed control problem by decentralized information. A decentralized strategy is obtained by feat of an MF type anticipated forward-backward stochastic differential delay equation (AFBSDDE) consistency condition. The discounting method with delay feature is employed to solve the consistency condition system. Finally, by some estimates of AFBSDDEs we derive the asymptotic social optimality.