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非对称信息博弈中的熵正则化均值方差投资组合

文章 arXiv papers · 作者: Yu-Jui Huang et al.
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总结

本文研究两名投资者如何选择均值方差投资组合，同时围绕相对财富展开竞争。一名投资者了解真实的股票动态；另一名则必须根据观察到的市场变化进行推断。两人的决策相互关联，因为每位投资者都会将期末财富与两人平均值进行比较；信息充分的投资者担任领导者，信息不完全的投资者则作为跟随者作出回应。

为了限制信息泄露，领导者使用熵正则化目标函数随机化其行动。跟随者能看到实际成交，但看不到产生这些交易的策略，因此其目标取决于观察到的路径。在理想化的连续观察设定下，论文推导出一种均衡，其中跟随者作出线性响应，领导者采取高斯分布的行动。在离散观察情况下，论文证明存在近似的 ε-均衡。这项研究属于理论分析：它报告均衡性质，而非实证投资组合表现；连续采样结果可能无法直接代表实际交易条件。

核心观点

  • 相对财富考量将两位投资者的均值方差决策联系起来。
  • 信息不完全的投资者担任跟随者，并根据观察到的领导者交易作出回应。
  • 熵正则化使信息充分的领导者采用随机化策略，以减少信息泄露。
  • 连续观察情况下，跟随者作出线性响应，领导者采取高斯分布的行动。
  • 离散采样情况下可得到近似的 Stackelberg 均衡。

标签

均值回归投资组合构建风险管理统计学
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# Mean-Variance Stackelberg Games with Asymmetric Information


# Mean-Variance Stackelberg Games with Asymmetric Information









This paper considers two investors who perform mean-variance portfolio selection with asymmetric information: one knows the true stock dynamics, while the other has to infer the true dynamics from observed stock evolution. Their portfolio selection is interconnected through relative performance concerns, i.e., each investor is concerned about not only her terminal wealth, but how it compares to the average terminal wealth of both investors. We model this as Stackelberg competition: the partially-informed investor (the "follower") observes the trading behavior of the fully-informed investor (the "leader") and decides her trading strategy accordingly; the leader, anticipating the follower's response, in turn selects a trading strategy that best suits her objective. To prevent information leakage, the leader adopts a randomized strategy selected under an entropy-regularized mean-variance objective, where the entropy regularizer quantifies the randomness of a chosen strategy. The follower, on the other hand, observes only the actual trading actions of the leader (sampled from the randomized strategy), but not the randomized strategy itself. Her mean-variance objective is thus a random field, in the form of an expectation conditioned on a realized path of the leader's trading actions. In the idealized case of continuous sampling of the leader's trading actions, we derive a Stackelberg equilibrium where the follower's trading strategy depends linearly on the actual trading actions of the leader and the leader samples her trading actions from Gaussian distributions. In the realistic case of discrete sampling of the leader's trading actions, the above becomes an $ε$-Stackelberg equilibrium.

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。