Estimation of the Adjusted Standard-deviatile for Extreme Risks

2024/11/11 by Haoyu Chen, Chen, Haoyu, Tiantian Mao +3 · 1 citation
Decision Sciences · #FOS: Economics and business #FOS: Mathematics #Risk Management (q-fin.RM) #Risk and Safety Analysis #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2411.07203

openalex publication_date 2024/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we modify the Bayes risk for the expectile, the so-called variantile risk measure, to better capture extreme risks. The modified risk measure is called the adjusted standard-deviatile. First, we derive the asymptotic expansions of the adjusted standard-deviatile. Next, based on the first-order asymptotic expansion, we propose two efficient estimation methods for the adjusted standard-deviatile at intermediate and extreme levels. By using techniques from extreme value theory, the asymptotic normality is proved for both estimators. Simulations and real data applications are conducted to examine the performance of the proposed estimators.

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