| 郝 涛.带有终端限制的平均场正倒向随机时滞控制系统的最大值原理以及在平均场对策中indent的应用[J].数学年刊A辑,2020,41(3):331~356 |
| 带有终端限制的平均场正倒向随机时滞控制系统的最大值原理以及在平均场对策中indent的应用 |
| Maximum Principle for Mean-Field Forward-Backward Stochastic Delay Control System with Terminal State Constraints and Application to Mean-Field Game |
| 投稿时间：2017-08-30 修订日期：2020-05-17 |
| DOI：10.16205/j.cnki.cama.2020.0024 |
| 中文关键词: 平均场正倒向时滞控制系统, 随机最大值原理, 终端扰动方法, Ekeland 变分, 平均场对策 |
| 英文关键词:Mean-Field forward-backward delay control system, Stochastic maximum principle, Terminal perturbation approach, Ekeland’s variational, Mean-Field game |
| 基金项目:国家自然科学基金 (No.,71671104, No.,11871309, No.,11801315, No.,11801317, No.,71803097),教育部人文社会科学项目(No.,16YJA910003), 山东省自然科学基金(No.,ZR2018QA001, No.,ZR2019MA013),山东省高等学校科技计划项目(No.,J17KA162, No.,J17KA163), 山东财经大学金融统计和风险管理团队,山东省高等学校青创科技计划(No.,2019KJI011) |
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| 中文摘要: |
| 研究带有时滞和终端状态限制的平均场正倒向随机控制系统的一个最优控制问题.驱动系统的系数依赖于解、解的时滞以及它们的分布. 利用Lions导数,终端扰动方法以及Ekeland变分原则, 得到了两种随机最大值原理.通过研究一个线性二次问题和一个生产-消费最优选取的平均场对策问题, 对这一理论结果进行了阐述说明. |
| 英文摘要: |
| This paper concerns a stochastic optimal control problem of a mean-field forwardbackward control system with delay and terminal state constraints. The coefficients of driving system depend on the solution, delay of the solution and all of their laws. Making use of the Lions’ derivative, terminal perturbation approach and Ekeland’s variational principle,two stochastic maximum principles involving law are obtained. As applications of the theoretical results, a linear-quadratic problem and a mean-field game of production-consumption choice optimization problem are investigated. |
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