英文标题：
《Backward SDEs for Control with Partial Information》
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作者：
Andrew Papanicolaou
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最新提交年份：
2018
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英文摘要：
This paper considers a non-Markov control problem arising in a financial market where asset returns depend on hidden factors. The problem is non-Markov because nonlinear filtering is required to make inference on these factors, and hence the associated dynamic program effectively takes the filtering distribution as one of its state variables. This is of significant difficulty because the filtering distribution is a stochastic probability measure of infinite dimension, and therefore the dynamic program has a state that cannot be differentiated in the traditional sense. This lack of differentiability means that the problem cannot be solved using a Hamilton-Jacobi-Bellman (HJB) equation. This paper will show how the problem can be analyzed and solved using backward stochastic differential equations (BSDEs), with a key tool being the problem\'s dual formulation.
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中文摘要：
本文考虑一个金融市场中的非马尔可夫控制问题，其中资产收益取决于隐藏因素。该问题是非马尔可夫问题，因为需要非线性滤波对这些因素进行推理，因此相关的动态程序有效地将滤波分布作为其状态变量之一。这是非常困难的，因为过滤分布是一个无限维的随机概率度量，因此动态程序具有传统意义上无法区分的状态。这种可微性的缺乏意味着这个问题无法用汉密尔顿-雅可比-贝尔曼（HJB）方程来解决。本文将展示如何使用倒向随机微分方程（BSDE）分析和解决该问题，关键工具是该问题的对偶公式。
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分类信息：

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
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