英文标题：
《Expert Opinions and Logarithmic Utility Maximization for Multivariate
Stock Returns 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：
2016
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英文摘要：
This paper investigates optimal trading strategies in a financial market with multidimensional stock returns where the drift is an unobservable multivariate Ornstein-Uhlenbeck process. Information about the drift is obtained by observing stock returns and expert opinions. The latter provide unbiased estimates on the current state of the drift at discrete points in time. The optimal trading strategy of investors maximizing expected logarithmic utility of terminal wealth depends on the filter which is the conditional expectation of the drift given the available information. We state filtering equations to describe its dynamics for different information settings. Between expert opinions this is the Kalman filter. The conditional covariance matrices of the filter follow ordinary differential equations of Riccati type. We rely on basic theory about matrix Riccati equations to investigate their properties. Firstly, we consider the asymptotic behaviour of the covariance matrices for an increasing number of expert opinions on a finite time horizon. Secondly, we state conditions for the convergence of the covariance matrices on an infinite time horizon with regularly arriving expert opinions. Finally, we derive the optimal trading strategy of an investor. The optimal expected logarithmic utility of terminal wealth, the value function, is a functional of the conditional covariance matrices. Hence, our analysis of the covariance matrices allows us to deduce properties of the value function.
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中文摘要：
本文研究了具有多维股票收益率的金融市场中的最优交易策略，其中漂移是一个不可观测的多元Ornstein-Uhlenbeck过程。通过观察股票收益率和专家意见，可以获得有关漂移的信息。后者提供了离散时间点漂移当前状态的无偏估计。投资者最大化终端财富预期对数效用的最优交易策略取决于过滤器，该过滤器是给定可用信息的漂移条件预期。我们通过状态滤波方程来描述其在不同信息设置下的动态特性。在专家意见之间，这是卡尔曼滤波器。滤波器的条件协方差矩阵遵循Riccati型常微分方程。我们依靠矩阵Riccati方程的基本理论来研究它们的性质。首先，我们考虑在有限时间范围内，越来越多的专家意见的协方差矩阵的渐近行为。其次，我们陈述了协方差矩阵在无限时间范围内收敛的条件，并给出了规则到达的专家意见。最后，我们推导了投资者的最优交易策略。终端财富的最优期望对数效用值函数是条件协方差矩阵的函数。因此，我们对协方差矩阵的分析允许我们推断值函数的性质。
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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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