Risk statistic is a critical factor not only for risk analysis but also for financial application. However, the traditional risk statistics may fail to describe the characteristics of regulator-based risk. In this paper, we consider the regulator-based risk statistics for portfolios. By further developing the properties related to regulator-based risk statistics, we are able to derive dual representation for such risk.

中文翻译：

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基于监管机构的投资组合风险统计

风险统计不仅是风险分析的关键因素，也是财务应用的关键因素。但是，传统的风险统计可能无法描述基于监管机构的风险的特征。在本文中，我们考虑了基于监管机构的投资组合风险统计。通过进一步开发与基于监管机构的风险统计相关的属性，我们可以得出此类风险的双重表示。