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In this paper, we study the general notions of upper and lower variances, which were initially introduced by Peter Walley for the bounded random variables. The properties of upper and lower variances and new formulas for calculation of them are provided. We take US markets for case study, which shows that the upper variance would be a useful tool to provide the risk management in the state or national level for the predication of (financial) systemic risk management by providing worst indicators to prepare the necessary implementation for the worst markets to coming in the practice.

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Applying the New Concept of Variances with Uncertainty to Cover the Worst Markets

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  • 发表日期：

    2025年

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  • Shan Li,
  • Xinpeng Li,
  • George Xianzhi Yuan

摘要

In this paper, we study the general notions of upper and lower variances, which were initially introduced by Peter Walley for the bounded random variables. The properties of upper and lower variances and new formulas for calculation of them are provided. We take US markets for case study, which shows that the upper variance would be a useful tool to provide the risk management in the state or national level for the predication of (financial) systemic risk management by providing worst indicators to prepare the necessary implementation for the worst markets to coming in the practice.