We consider the optimal control problem for a linear conditional McKean-Vlasov equation with quadratic cost functional. The coefficients of the system and the weighting matrices in the cost functional are allowed to be adapted processes with respect to the common noise filtration. Semi closed-loop strategies are introduced, and following the dynamic programming approach in (Pham and Wei, Dynamic programming for optimal control of stochastic McKean-Vlasov dynamics, 2016), we solve the problem and characterize time-consistent optimal control by means of a system of decoupled backward stochastic Riccati differential equations. We present several financial applications with explicit solutions, and revisit, in particular, optimal tracking problems with price impact, and the conditional mean-variance portfolio selection in an incomplete market model.

中文翻译：

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随机系数的条件McKean-Vlasov方程的线性二次最优控制及应用

我们考虑具有二次成本函数的线性条件McKean-Vlasov方程的最优控制问题。系统的系数和成本函数中的权重矩阵可以针对常见的噪声过滤进行调整。引入半闭环策略，并遵循（Pham and Wei，随机McKean-Vlasov动力学的最优控制的动态编程，2016）中的动态规划方法，我们解决了该问题并通过a来描述时间一致的最优控制解耦后向随机Riccati微分方程组。我们提出了具有明确解决方案的几种金融应用程序，并进行了重新审查，尤其是在价格不完全的市场模型中具有价格影响的最佳跟踪问题以及有条件的均方差投资组合选择。