高斯漂移市场中的专家意见与对数效用最大化
Expert Opinions and Logarithmic Utility Maximization in a Market with Gaussian Drift
摘要：
本文研究了金融市场中的最优投资组合策略，其中股票收益率的漂移是由不可观测的高斯均值回复过程驱动的。关于这一过程的信息是从观察股票收益和专家意见中获得的。后者在离散时间点提供漂移的当前状态的无偏估计。然而，漂移只能部分观察到，最佳估计是由给定可用信息的条件期望给出的，即，通过过滤器。我们提供的过滤器方程的模型与专家意见，并详细推导出的条件方差的性质。对于最大化其投资组合的期望对数效用的投资者，我们得到了最优策略，明确在不同的设置为可用的信息。最优期望效用，即控制问题的价值函数，取决于条件方差。条件方差的界和渐近结果被用来导出值函数的界和渐近性质。最后用数值例子说明了结果。
英文摘要：
This paper investigates optimal portfolio strategies in a financial market where the drift of the stock returns is driven by an unobserved Gaussian mean reverting process. Information on this process is obtained from observing stock returns and expert opinions. The latter provide at discrete time points an unbiased estimate of the current state of the drift. Nevertheless, the drift can only be observed partially and the best estimate is given by the conditional expectation given the available information, i.e., by the filter. We provide the filter equations in the model with expert opinion and derive in detail properties of the conditional variance. For an investor who maximizes expected logarithmic utility of his portfolio, we derive the optimal strategy explicitly in different settings for the available information. The optimal expected utility, the value function of the control problem, depends on the conditional variance. The bounds and asymptotic results for the conditional variances are used to derive bounds and asymptotic properties for the value functions. The results are illustrated with numerical examples.
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