The optimal allocation of assets has been widely discussed with the theoretical analysis of risk measures, and pessimism is one of the most attractive approaches beyond the conventional optimal portfolio model. 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 a computationally tractable model. In this study, we propose an integral of $\alpha$-risk called the \textit{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. Real data analysis of three stock datasets (S\&P500, CSI500, KOSPI200) demonstrates the usefulness of the proposed risk and portfolio model.

翻译：资产最优配置在风险测度的理论分析中已得到广泛探讨，而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。α-风险在推导一类广泛的悲观最优投资组合中发挥着关键作用。然而，由于缺乏计算上易于处理的模型，评估由悲观风险测度下的最优投资组合仍具挑战性。本研究提出一种称为"统一悲观风险"的α-风险积分形式，并开发了基于该风险获得最优投资组合的计算算法。进一步地，我们从三个不同视角——分位数回归、恰当评分规则和分布鲁棒优化——研究了所提风险的理论性质。基于三个股票数据集（S&P500、CSI500、KOSPI200）的真实数据分析证明了所提风险及投资组合模型的有效性。