Measuring the risks associated with financial activities has long been a central focus for banks, insurance companies, and other institutions. Risk management is now essential for assessing exposure to the various risk factors inherent in financial transactions. Regulations across different sectors require the implementation of procedures to calculate the riskiness of financial assets as accurately as possible. The regulations outlined in the Basel Accords for the banking sector are a prime example, as they explicitly require the use of quantitative tools like risk measures. The best-known example of this tool is Value at Risk.

As a result, since the end of the last century, the number of studies on risk measures in the academic literature on financial mathematics has steadily increased. Starting with a precise, axiomatic definition in the renowned 1999 paper by P. Artzner, F. Delbaen, J.-M. Eber, and D. Heath [1], the aim is to provide an in-depth analysis of the key properties a risk measure can possess. These properties are essential for capturing important financial concepts, such as diversification.

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