A General Stochastic Maximum Principle for Mean-Field Controls with Regime Switching
A General Stochastic Maximum Principle for Mean-Field Controls with Regime Switching
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DOI：
10.1007/s00245-021-09747-x
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发表时间：
2021-01
影响因子：
1.8
通讯作者：
S. L. Nguyen;G. Yin;D. Nguyen
中科院分区：
文献类型：
--
作者：
S. L. Nguyen;G. Yin;D. Nguyen
本文着眼于具有平均场相互作用的状态转换扩散，致力于获得一般最大值原理。其主要特点是将条件平均场应用于受控动态系统和优化过程。利用具有状态切换和条件平均场的正向和倒向随机微分方程对变分和伴随方程进行了分析。在不假设控制空间凸性的情况下，得到了最优性的必要条件。最后，给出了一个具有状态转换的条件均值-方差投资组合问题的例子，说明了最优性的充分条件。
Focusing on regime-switching diffusions with mean-fields interactions, this paper is devoted to obtaining a general maximum principle. A main feature is that conditional mean-field is used in the controlled dynamic systems and the optimization process. Analysis of variational and adjoint equations using forward and backward stochastic differential equations with regime-switching and conditional mean-field is carried out. Necessary conditions for optimality are obtained without assuming the convexity of the control space. An example on conditional mean-variance portfolio selection with regime switching is given to illustrate the sufficient conditions for optimality.