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.

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The portfolio are a critical factor not only in risk analysis, but also in insurance and financial applications. In this paper, we consider a special class of risk statistics from the perspective of regulator. This new risk statistic can be uesd for the quantification of portfolio risk. By further developing the properties related to regulator-based risk statistics, we are able to derive dual representation for them. Finally, examples are also given to demonstrate the application of this risk statistic.

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