英文标题：
《Linear quadratic optimal control of conditional McKean-Vlasov equation
with random coefficients and applications *》
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作者：
Huy\\^en Pham (LPMA, CREST)
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最新提交年份：
2017
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英文摘要：
We consider the optimal control problem for a linear conditional McKean-Vlasov equation with quadratic cost functional. The coefficients of the system and the weigh-ting 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 [32], 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 incomplete market model.
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中文摘要：
研究了一类具有二次成本泛函的线性条件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根据公共噪声过滤过程进行调整。引入了半闭环策略，并遵循[32]中的动态规划方法，通过解耦的倒向随机Riccati微分方程组来解决问题并刻画时间一致性最优控制。我们给出了几个具有显式解的金融应用，并特别讨论了具有价格影响的最优跟踪问题，以及不完全市场模型中的条件均值-方差投资组合选择。
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分类信息：

一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Mathematics 数学
二级分类：Optimization and Control 优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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