英文标题：
《On a class of path-dependent singular stochastic control problems》
---
作者：
Romuald Elie and Ludovic Moreau and Dylan Possama\\\"i
---
最新提交年份：
2018
---
英文摘要：
This paper studies a class of non$-$Markovian singular stochastic control problems, for which we provide a novel probabilistic representation. The solution of such control problem is proved to identify with the solution of a $Z-$constrained BSDE, with dynamics associated to a non singular underlying forward process. Due to the non$-$Markovian environment, our main argumentation relies on the use of comparison arguments for path dependent PDEs. Our representation allows in particular to quantify the regularity of the solution to the singular stochastic control problem in terms of the space and time initial data. Our framework also extends to the consideration of degenerate diffusions, leading to the representation of the solution as the infimum of solutions to $Z-$constrained BSDEs. As an application, we study the utility maximisation problem with transaction costs for non$-$Markovian dynamics.
---
中文摘要：
研究了一类非$-$马尔可夫奇异随机控制问题，给出了一种新的概率表示。证明了该控制问题的解与$Z-$约束BSDE的解是一致的，其动力学与非奇异的潜在正向过程有关。由于非$-$马尔可夫环境，我们的主要论证依赖于对路径相关偏微分方程使用比较参数。我们的表示特别允许根据空间和时间初始数据量化奇异随机控制问题解的规律性。我们的框架还扩展到退化扩散的考虑，导致将解表示为$Z-$约束BSDE解的下确界。作为一个应用，我们研究了非$-$马尔可夫动态下具有交易费用的效用最大化问题。
---
分类信息：

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
--
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
--
一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
--

---
PDF下载：
-->