郝涛. 风险敏感性平均场控制的一个二阶必要条件[J]. 应用概率统计, 2024, 40(3): 433-451. DOI: 10.3969/j.issn.1001-4268.2024.03.006
引用本文: 郝涛. 风险敏感性平均场控制的一个二阶必要条件[J]. 应用概率统计, 2024, 40(3): 433-451. DOI: 10.3969/j.issn.1001-4268.2024.03.006
HAO T. A second-order necessary condition for risk-sensitive mean-field type control [J]. Chinese J Appl Probab Statist, 2024, 40(3): 433−451. DOI: 10.3969/j.issn.1001-4268.2024.03.006
Citation: HAO T. A second-order necessary condition for risk-sensitive mean-field type control [J]. Chinese J Appl Probab Statist, 2024, 40(3): 433−451. DOI: 10.3969/j.issn.1001-4268.2024.03.006

风险敏感性平均场控制的一个二阶必要条件

A Second-Order Necessary Condition for Risk-Sensitive Mean-Field Type Control*

  • 摘要: 本文研究风险敏感性平均场控制的一个二阶必要条件. 介绍了一类新的分裂形式的一阶伴随方程, 这类方程在分析二阶伴随变量转换时更具有优势. 通过构造一类新的二阶伴随变量的转换, 证明风险敏感性平均场奇异控制的二阶最大值原理. 最后, 我们提供了一个解释性例子.

     

    Abstract: In this paper, we investigate the second-order necessary condition for risk-sensitive mean-field type control. A class of new split first-order adjoint equations is brought in, which demonstrates more superiorities in analysing the transformation of the second-order adjoint variables. By means of constructing a new transformation of the second-order adjoint variables, the second-order stochastic maximum principle of risk-sensitive mean-field type singular control is proved. Finally, an illustrative example is provided.

     

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