2025/04/28 by Baishuai Zuo, Zuo, Baishuai, Chuancun Yin +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Applications (stat.AP) #FOS: Computer and information sciences #FOS: Economics and business #Financial Risk and Volatility Modeling #Risk Management (q-fin.RM) #Statistical Distribution Estimation and Applications #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.2504.19725
openalex publication_date 2025/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we develop the lower and upper bounds of worst-case distortion riskmetrics and weighted entropy for unimodal, and symmetric unimodal distributions when mean and variance information are available. We also consider the sharp upper bounds of distortion riskmetrics and weighted entropy for symmetric distribution under known mean and variance. These results are applied to (weighted) entropies, shortfalls and other risk measures. Specifically, entropies include cumulative Tsallis past entropy, cumulative residual Tsallis entropy of order α, extended Gini coefficient, fractional generalized cumulative residual entropy, and fractional generalized cumulative entropy. Shortfalls include extended Gini shortfall, Gini shortfall, shortfall of cumulative residual entropy, and shortfall of cumulative residual Tsallis entropy. Other risk measures include nth-order expected shortfall, dual power principle and proportional hazard principle.