The optimality of allocating assets has been widely discussed with the theoretical analysis of risk measures. Pessimism is one of the most attractive approaches beyond the conventional optimal portfolio model, and the $\alpha$-risk plays a crucial role in deriving a broad class of pessimistic optimal portfolios. However, estimating an optimal portfolio assessed by a pessimistic risk is still challenging due to the absence of an available estimation model and a computational algorithm. In this study, we propose a version of integrated $\alpha$-risk called the uniform pessimistic risk and the computational algorithm to obtain an optimal portfolio based on the risk. Further, we investigate the theoretical properties of the proposed risk in view of three different approaches: multiple quantile regression, the proper scoring rule, and distributionally robust optimization. Also, the uniform pessimistic risk is applied to estimate the pessimistic optimal portfolio models for the Korean stock market and compare the result of the real data analysis. It is empirically confirmed that the proposed pessimistic portfolio presents a more robust performance than others when the stock market is unstable.

翻译：资产配置的最优性已在风险度量理论分析的背景下得到广泛讨论。悲观主义是超越传统最优投资组合模型最具吸引力的方法之一，而$\alpha$-风险在推导更广泛的悲观最优投资组合中扮演着关键角色。然而，由于缺乏可用的估计模型和计算算法，评估基于悲观风险的最优投资组合仍具挑战性。本研究提出了一种名为统一悲观风险的集成$\alpha$-风险变体，并开发了基于该风险获取最优投资组合的计算算法。进一步，我们从三个不同视角（多元分位数回归、恰当评分规则和分布鲁棒优化）探讨了所提风险的理论性质。此外，将统一悲观风险应用于韩国股票市场的悲观最优投资组合模型估计，并与实际数据分析结果进行比较。实证表明，当股票市场不稳定时，所提出的悲观投资组合展现出比其他模型更稳健的表现。