AI 中文总结
本文提出鲁棒平均场控制框架，将其应用于复合不确定性下的多维最优清盘问题，借助HJBI方程与先验估计证明相关方程适定性，解决了对应最优清盘问题。
AI 中文摘要
本文提出了一套用于鲁棒平均场控制问题的框架，该框架可描述在基础随机过程与确定性模型参数双重不确定性下的多维最优清盘问题。我们借助以概率测度为变量的哈密尔顿-雅可比-贝尔曼-艾萨克斯（HJBI）方程建立验证结果，其中哈密顿量非线性地包含了头寸与动量的联合分布。通过新颖的先验估计，我们证明了既非位移凸也非凹的一般或二次哈密顿量对应的HJBI方程适定性。该先验估计与适定性结果被推广应用于最优清盘问题，在此类问题中，我们允许哈密顿量具有线性增长的导数，并求解复合不确定性下受约束的多维线性二次最优清盘问题。
英文摘要
We provide a framework for robust mean field control problems that describe multi-dimensional optimal liquidation problems under uncertainty from both the underlying stochastic process and the deterministic model parameters. The verification results are established with Hamilton-Jacobi-Bellman-Isaacs (HJBI) equations where the variables are probability measures and the Hamiltonian nonlinearly involves the joint distribution of position and momentum. Using novel a priori estimates, we establish the well-posedness of the HJBI equations featuring general or quadratic Hamiltonians that are neither displacement convex nor concave in their momentum. The a priori estimates and well-posedness results are extended during their application to optimal liquidation problems, where we allow the Hamiltonian to have derivatives of linear growth and solve the constrained multi-dimensional linear quadratic optimal liquidation problem under composite uncertainty.
