跳至正文
返回文库全部文档

模型不确定性下的稳健组合增长

文章 arXiv papers · 作者: Constantinos Kardaras et al.
阅读原文

总结

本文研究在市场模型不确定时如何实现长期财富增长最大化。研究考虑受已知资产区域和瞬时协方差约束的模型，并增加一项稳定性条件：长期占用测度收敛至一个密度。提出这一条件的动机，是股票市场中按相对市值排名的稳定性。

在对这些输入作出最少假设的情况下，作者将稳健增长率与占用时间大偏差中的 Donsker–Varadhan 速率函数联系起来。他们还建立并明确刻画了一种交易策略，使其在所考虑的模型中实现这一速率。一个应用研究了按相对市值排名的漂移不确定性，并假定对称化后满足正则性条件。摘录介绍了理论结果及一项具体应用，但没有提供实证绩效测试或实际实现细节。

核心观点

  • 目标是在市场模型不确定的情况下实现投资者财富增长最大化。
  • 该模型类别固定资产区域和瞬时协变结构，同时要求占用测度保持稳定。
  • 稳健增长率与 Donsker–Varadhan 速率函数相关联。
  • 作者找到了在所纳入模型中实现稳健速率的策略。
  • 按市值排名的应用依赖正则性假设，且以理论形式呈现。

标签

投资组合构建风险管理统计学股票
全文
# Ergodic robust maximization of asymptotic growth


# Ergodic robust maximization of asymptotic growth









We consider the problem of robustly maximizing the growth rate of investor wealth in the presence of model uncertainty. Possible models are all those under which the assets' region $E$ and instantaneous covariation $c$ are known, and where additionally the assets are stable in that their occupancy time measures converge to a law with density $p$. This latter assumption is motivated by the observed stability of ranked relative market capitalizations for equity markets. We seek to identify the robust optimal growth rate, as well as a trading strategy which achieves this rate in all models. Under minimal assumptions upon $(E,c,p)$, we identify the robust growth rate with the Donsker-Varadhan rate function from occupancy time Large Deviations theory. We also prove existence of, and explicitly identify, the optimal trading strategy. We then apply our results in the case of drift uncertainty for ranked relative market capitalizations. Assuming regularity under symmetrization for the covariance and limiting density of the ranked capitalizations, we explicitly identify the robust optimal trading strategy in this setting.

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。