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

作　　者：郝涛[1] HAO Tao(School of Statistics and Mathematics,Shandong University of Finance and Economics,Jinan,250014,China)

机构地区：[1]山东财经大学统计与数学学院,济南250014

出　　处：《应用概率统计》2024年第3期433-451,共19页Chinese Journal of Applied Probability and Statistics

基　　金：supported by the Natural Science Foundation of Shandong Province(Grant Nos.ZR2020MA032,ZR2022MA029);the National Natural Science Foundation of China(Grant No.72171133);the high-quality course for postgraduate education in Shandong Province《Intermediate Econometrics(Graded Teaching)》(SDYKC21137).

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.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.

关 键 词：奇异最优控制 分裂形式的一阶伴随方程 二阶伴随方程 二阶最大值原理 风险敏感性 

分 类 号：O211.63[理学—概率论与数理统计]