arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2305.07166q-fin.MF
收藏

均值-方差投资组合选择的鲁棒均衡策略

Robust Equilibrium Strategy for Mean-Variance Portfolio Selection

Mengge Li, Shuaijie Qian, Chao Zhou

阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

AI总结：

本文在动态均值-方差框架下引入鲁棒控制，提出新的鲁棒均衡策略定义，证明相应PDE系统的经典解可导出该策略，并对特殊例子给出显式解。

摘要：

经典的均值-方差投资组合选择问题会导出时间不一致（预先承诺）的策略（参见 Zhou 和 Li (2000)）。为了克服这种时间不一致性，Basak 和 Chabakauri (2010) 引入了博弈论方法，并寻找（子博弈完美纳什）均衡策略，该策略通过相应的偏微分方程（PDE）系统求解。在他们的模型中，投资者完全知道资产的漂移率和波动率。然而，在现实中，投资者只能对它们进行估计，例如一个 95% 的置信区间。在这种情况下，一些文献（例如 Pham、Wei 和 Zhou (2022)）在最差参数下推导出最优预先承诺策略，这就是鲁棒控制。在引入鲁棒控制时，均衡策略与 PDE 系统之间的关系尚未得到证明。在本文中，我们考虑一个一般的动态均值-方差框架，并提出了一种新颖的鲁棒均衡策略定义。在我们的定义下，相应 PDE 系统的一个经典解蕴含着一个鲁棒均衡策略。然后，我们针对一些特殊例子进行了显式求解。

英文摘要：

The classical mean-variance portfolio selection problem induces time-inconsistent (precommited) strategies (see Zhou and Li (2000)). To overcome this time-inconsistency, Basak and Chabakauri (2010) introduce the game theoretical approach and look for (sub-game perfect Nash) equilibrium strategies, which is solved from the corresponding partial differential equations (PDE) system. In their model, the investor perfectly knows the drift and volatility of the assets. However, in reality investors only have an estimate on them, e.g, a 95% confidence interval. In this case, some literature (e.g., Pham, Wei and Zhou (2022)) derives the optimal precommited strategy under the worst parameters, which is the robust control. The relation between the equilibrium strategy and the PDE system has not been justified when incorporating robust control. In this paper, we consider a general dynamic mean-variance framework and propose a novel definition of the robust equilibrium strategy. Under our definition, a classical solution to the corresponding PDE system implies a robust equilibrium strategy. We then explicitly solve for some special examples.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑