摘要
The Kelly strategy is a common approach in portfolio optimization problems that aims to maximize the expected portfolio growth rate in the long term.Its computation requires complete knowledge of the asset return distribution,which is obviously not observable,but can be inferred from sample data.Motivated by recent developments in data-driven optimization methods,we propose a new class of coherent Wasserstein data-driven Kelly portfolio optimization models.In particular,we establish a class of ambiguity sets based on coherent Wasserstein metrics,and these new metrics can strike a good balance between robustness and data-drivenness,thus providing richer choices for ambiguity set design.The Kelly portfolio optimization model,which is data-driven and based on coherent Wasserstein balls,can be solved efficiently as a finite-dimensional convex program.This model also provides a robust data-driven solution.In addition,we numerically investigate the proposed model and find that it outperforms the type-1 Wasserstein-Kelly portfolio,especially the classical Kelly portfolio.Moreover,it indicates that we can obtain a portfolio with higher final value and stability,especially in controlling volatility and maximum drawdown.
Kelly策略是投资组合优化问题中的一种常见方法,旨在最大化投资组合的长期预期增长率。它的计算需要对资产收益分布有完整的了解,而这显然是不可观测的,但能从样本数据中推断而来。受数据驱动优化方法最新发展的启发,我们提出了一类新的一致Wasserstein数据驱动Kelly投资组合优化模型。特别地,我们建立了一个基于一致Wasserstein度量的模糊集,这些新度量可以在鲁棒性和数据驱动性之间取得良好的平衡,从而为模糊集的设计提供了更丰富的选择。Kelly投资组合优化模型以数据为驱动,并且基于一致Wasserstein球,其可以作为有限维的凸程序有效求解。该模型还提供了一个鲁棒的数据驱动解决方案。此外,我们对提出的模型进行了数值研究,发现它优于1型Wasserstein-Kelly投资组合,尤其是经典的Kelly投资组合。另外,它还表明我们可以获得具有更高最终价值和稳定性的投资组合,特别是在控制波动性和最大回撤方面。
基金
supported by the National Natural Science Foundation of China(12401625)
the China Postdoctoral Science Foundation(2024M753074)
the Postdoctoral Fellowship Program of CPSF(GZC20232556)
the Fundamental Research Funds for the Central Universities(WK2040000108).
