数学金融中的三个过滤问题

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摘要翻译：
在数学金融学中使用过滤理论的三种情况下，详细说明了不同的层次。这三个问题源于以下不同的工作：1）由观察到的双边汇率消息估计随机波动率模型，由R.Mahieu和P.Schotman提出；2）用状态空间方法估计利率期限结构的多因素CIR模型。Geyer和S.Pichler；3）金融衍生品定价中部分观测下的风险最小化套期保值策略，P.Fischer，E.Platen，W.J.Runggaldier；在第一个问题中，我们提出了一种新的基于几何的非线性滤波技术来估计由观察到的双边汇率波动率时间序列。这里使用的模型是随机波动率模型。我们提出的滤波器被称为投影滤波器，并给出了这类滤波器的简要推导。详细介绍了第二个问题，并暗示了不同过滤技术的可能使用。事实上，在2）和部分文献中用于这个问题的滤波器可以解释为投影滤波器，我们将对如何构造更一般的和可能更合适的投影滤波器进行一些评论。第三个问题只在短时间内提出。
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英文标题：
《On three filtering problems arising in mathematical finance》
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作者：
Damiano Brigo and Bernard Hanzon
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最新提交年份：
2008
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分类信息：

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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英文摘要：
  Three situations in which filtering theory is used in mathematical finance are illustrated at different levels of detail. The three problems originate from the following different works: 1) On estimating the stochastic volatility model from observed bilateral exchange rate news, by R. Mahieu, and P. Schotman; 2) A state space approach to estimate multi-factors CIR models of the term structure of interest rates, by A.L.J. Geyer, and S. Pichler; 3) Risk-minimizing hedging strategies under partial observation in pricing financial derivatives, by P. Fischer, E. Platen, and W. J. Runggaldier; In the first problem we propose to use a recent nonlinear filtering technique based on geometry to estimate the volatility time series from observed bilateral exchange rates. The model used here is the stochastic volatility model. The filters that we propose are known as projection filters, and a brief derivation of such filters is given. The second problem is introduced in detail, and a possible use of different filtering techniques is hinted at. In fact the filters used for this problem in 2) and part of the literature can be interpreted as projection filters and we will make some remarks on how more general and possibly more suitable projection filters can be constructed. The third problem is only presented shortly.
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PDF链接：
https://arxiv.org/pdf/0812.4050

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关键词：数学金融 used 方法 技术 利率 different