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基于专家观点与均值回归漂移的对数效用交易

文章 arXiv papers · 作者: Jörn Sass et al.
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总结

当多变量股票收益漂移不可直接观测，且按照奥恩斯坦–乌伦贝克过程演变时，本文推导了一个旨在最大化预期对数效用的投资者的最优投资组合策略。投资者根据观察到的收益以及专家观点来了解漂移；专家观点是在离散时点到达的无偏估计。策略取决于投资者现有信息所对应的条件预期漂移。

在专家更新之间，估计值遵循卡尔曼滤波，而其条件协方差通过矩阵黎卡提方程演变。分析研究了在有限期限内专家观点变得更加频繁时，以及在无限期限内定期更新时，这些协方差的变化情况。价值函数取决于协方差矩阵，将信息质量与最优预期效用联系起来。本文提出数学模型并分析其收敛性，但没有实证评估；实际表现取决于所假设的漂移动态，以及专家估计的可靠性和时点。

核心观点

  • 未观测的多变量收益漂移被建模为均值回归的奥恩斯坦–乌伦贝克过程。
  • 投资者在离散时点利用收益和无偏专家观点更新漂移估计。
  • 专家意见更新之间的估计动态由卡尔曼滤波描述，协方差则由黎卡提方程控制。
  • 最优对数效用策略取决于经过滤波的条件预期漂移。
  • 分析将协方差收敛与价值函数联系起来，但没有报告实证交易结果。

标签

股票统计学投资组合构建仓位规模
全文
# Expert Opinions and Logarithmic Utility Maximization for Multivariate Stock Returns with Gaussian Drift


# Expert Opinions and Logarithmic Utility Maximization for Multivariate Stock Returns with Gaussian Drift









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.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: abstract CC0

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。