发表机构
University of Waterloo; University of Science and Technology of China（滑铁卢大学; 中国科学技术大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出在奖励-惩罚机制下最小化最坏情况条件风险价值的稳健投资组合模型，推导闭式解并应用于两种分布集，实证表明其优于现有模型并揭示收益与风险权衡。
AI 中文摘要
在本文中，我们通过将奖励和惩罚机制纳入投资组合管理，提出了稳健的投资组合选择模型。我们假设投资组合中基础风险资产损失的联合分布是不确定的，但位于一个多元分布集内。我们的目标是通过最小化在奖励和惩罚机制和分布不确定性下投资组合损失的最坏情况条件风险价值（CVaR）来确定最优投资组合配置。我们的模型也可用于研究如何在投资组合管理中平衡投资组合损失与其相关的下行风险的问题。我们首先推导出在奖励-惩罚机制下最坏情况CVaR的显式闭式表达式，该表达式推广了关于最坏情况CVaR的几个现有模型和结果，例如Jagannathan (1977)、Chen et al. (2011)和Cai et al. (2024)中研究的那些。然后，我们应用该表达式，在经典的基于均值-协方差的多元分布集和Kang et al. (2019)中引入的广义基于均值-协方差的多元分布集下，获得使最坏情况CVaR最小化的最优投资组合配置。此外，我们利用真实市场数据来说明所提出的模型及相应的最优投资组合配置在投资组合管理中的应用。我们的实证实验表明，基于所提出模型的投资组合有潜力优于基于几个现有相关模型的投资组合。此外，结果表明，将下行风险纳入投资组合损失有助于更好地管理风险，并且可以实现比单独考虑下行风险或投资组合损失更高的投资回报。此外，我们的实验揭示了提高预期投资组合回报与控制最坏情况投资组合CVaR之间的权衡。
英文摘要
In this paper, we present robust portfolio selection models by incorporating a reward and penalty mechanism into portfolio management. We assume that the joint distribution of the losses of the underlying risky assets in a portfolio is uncertain but lies within a multivariate distribution set. Our goal is to identify optimal portfolio allocations by minimizing the worst-case conditional value-at-risk (CVaR) of portfolio loss under the reward and penalty mechanism and distribution uncertainty. Our models can also be used to investigate the problem of how to balance portfolio losses with their associated downside risk in portfolio management. We first derive an explicit closed-form expression for the worst-case CVaR under the reward-penalty mechanism, which generalizes several existing models and results regarding the worst-case CVaR, such as those studied in Jagannathan (1977), Chen et al. (2011), and Cai et al. (2024). We then apply this expression to obtain optimal portfolio allocations that minimize the worst-case CVaR under both a classical mean-covariance-based multivariate distribution set and a generalized mean-covariance-based multivariate distribution set introduced in Kang et al. (2019). Additionally, we utilize real market data to illustrate the application of the proposed models and the corresponding optimal portfolio allocations in portfolio management. Our empirical experiments show that portfolios based on the proposed models have the potential to outperform those based on several existing related models. Furthermore, the results demonstrate that incorporating downside risk into portfolio loss helps better manage risk and can achieve higher investment returns than considering either downside risk or portfolio loss alone. Moreover, our experiments reveal the trade-off between improving expected portfolio return and controlling the worst-case portfolio CVaR.
