英文标题：
《Diffusion Approximations for Expert Opinions in a Financial Market with
Gaussian Drift》
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作者：
J\\\"orn Sass, Dorothee Westphal, Ralf Wunderlich
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最新提交年份：
2020
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英文摘要：
This paper investigates a financial market where returns depend on an unobservable Gaussian drift process. While the observation of returns yields information about the underlying drift, we also incorporate discrete-time expert opinions as an external source of information. For estimating the hidden drift it is crucial to consider the conditional distribution of the drift given the available observations, the so-called filter. For an investor observing both the return process and the discrete-time expert opinions, we investigate in detail the asymptotic behavior of the filter as the frequency of the arrival of expert opinions tends to infinity. In our setting, a higher frequency of expert opinions comes at the cost of accuracy, meaning that as the frequency of expert opinions increases, the variance of expert opinions becomes larger. We consider a model where information dates are deterministic and equidistant and another model where the information dates arrive randomly as the jump times of a Poisson process. In both cases we derive limit theorems stating that the information obtained from observing the discrete-time expert opinions is asymptotically the same as that from observing a certain diffusion process which can be interpreted as a continuous-time expert. We use our limit theorems to derive so-called diffusion approximations of the filter for high-frequency discrete-time expert opinions. These diffusion approximations are extremely helpful for deriving simplified approximate solutions of utility maximization problems.
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中文摘要：
本文研究了一个收益率依赖于不可观测高斯漂移过程的金融市常虽然对收益率的观察产生了关于潜在漂移的信息，但我们也将离散时间专家意见作为外部信息来源。对于估计隐藏漂移，考虑给定可用观测值漂移的条件分布至关重要，即所谓的滤波器。对于同时观察收益过程和离散时间专家意见的投资者，我们详细研究了当专家意见到达频率趋于无穷大时滤波器的渐近行为。在我们的环境中，专家意见的频率越高，其准确性就越低，这意味着随着专家意见频率的增加，专家意见的差异就越大。我们考虑一个模型，其中信息日期是确定的和等距的，另一个模型，其中信息日期随机到达，作为泊松过程的跳跃时间。在这两种情况下，我们都推导出极限定理，说明从观察离散时间专家意见获得的信息与从观察某个可以解释为连续时间专家的扩散过程获得的信息是渐近相同的。我们使用极限定理推导出高频离散时间专家意见滤波器的所谓扩散近似。这些扩散近似对于导出效用最大化问题的简化近似解非常有用。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Portfolio Management 项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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