相关噪声下随机最优控制问题的最大值原理
Maximum Principles for Stochastic Optimal Control Problems with Correlated Noises
摘要: 本文研究了一类延迟信息下的随机最优控制问题，其中控制过程是关于延迟信息的滤子流适应，且系统中多个噪声不独立具有相关性。本文首先利用凸变分法建立必要最大值原理，进一步假设哈密尔顿函数和终端效用函数具有凹性得到充分最大值原理，最后将得到的充分必要最大值原理应用于一类资产组合配置问题中的均值–方差模型。
Abstract: This paper studies a class of stochastic optimal control problems with delayed information, where the control process is adapted to the delayed filtration, which describes the delayed information, and that the noises in the system are not independent but correlated. The necessary maximum principle is established using the convex variational method. Furthermore, the sufficient maximum principle is given on the assumption that the Hamiltonian function and the terminal utility function are concave. Finally, the obtained maximum principles are applied to the mean-variance model for a class of asset portfolio allocation problems.
文章引用：解斯雯, 王岩. 相关噪声下随机最优控制问题的最大值原理[J]. 动力系统与控制, 2025, 14(2): 139-150. https://doi.org/10.12677/dsc.2025.142015

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