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随机因子与漂移不确定性下的稳健投资组合增长

文章 arXiv papers · 作者: Balint Binkert et al.
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总结

本文研究预期资产收益不确定时的投资组合增长优化问题。研究对象是一个不完全、高维市场，其中资产价格取决于随机因子。该框架不完全固定漂移，而是通过共同的波动率结构、长期联合分布以及特定的因子动态（包括遍历性条件）来约束可接受模型。

作者刻画稳健增长率和最坏情况下的可接受模型，并通过偏微分方程推导增长最优策略。他们认为，纳入随机因子可以改善稳健增长，并用数值示例说明理论，其中包括将价差作为建模资产的配对交易。结果取决于所选模型类别及其遍历性和动态假设；摘要没有给出改善幅度的数值，也没有实盘交易证据。

核心观点

  • 该框架通过稳健增长优化，处理资产收益漂移不确定所带来的敏感性。
  • 可接受模型对波动率、长期联合密度和随机因子动态作出约束。
  • 在这一受约束的模型类别中，作者刻画了稳健增长率和最坏情况模型。
  • 作者使用偏微分方程刻画稳健增长最优策略。
  • 作者报告称，使用随机因子可以改善稳健增长，包括在配对交易示例中。

标签

统计学风险管理投资组合构建配对交易
全文
# Stochastic factors can matter: improving robust growth under ergodicity


# Stochastic factors can matter: improving robust growth under ergodicity









Drifts of asset returns are notoriously difficult to model accurately and, yet, trading strategies obtained from portfolio optimization are very sensitive to them. To mitigate this well-known phenomenon we study robust growth-optimization in a high-dimensional incomplete market under drift uncertainty of the asset price process $X$, under an additional ergodicity assumption, which constrains but does not fully specify the drift in general. The class of admissible models allows $X$ to depend on a multivariate stochastic factor $Y$ and fixes (a) their joint volatility structure, (b) their long-term joint ergodic density and (c) the dynamics of the stochastic factor process $Y$. A principal motivation of this framework comes from pairs trading, where $X$ is the spread process and models with the above characteristics are commonplace. Our main results determine the robust optimal growth rate, construct a worst-case admissible model and characterize the robust growth-optimal strategy via a solution to a certain partial differential equation (PDE). We demonstrate that utilizing the stochastic factor leads to improvement in robust growth complementing the conclusions of the previous study by Itkin et. al. (arXiv:2211.15628 [q-fin.MF], forthcoming in $\textit{Finance and Stochastics}$), which additionally robustified the dynamics of the stochastic factor leading to $Y$-independent optimal strategies. Our analysis leads to new financial insights, quantifying the improvement in growth the investor can achieve by optimally incorporating stochastic factors into their trading decisions. We illustrate our theoretical results on several numerical examples including an application to pairs trading.

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。