Risk measure

In financial mathematics, a risk measure is used to determine the amount of an asset or set of assets (traditionally currency) to be kept in reserve. The purpose of this reserve is to make the risks taken by financial institutions, such as banks and insurance companies, acceptable to the regulator. In recent years attention has turned towards convex and coherent risk measurement.

A risk measure is defined as a mapping from a set of random variables to the real numbers. This set of random variables represents portfolio returns. The common notation for a risk measure associated with a random variable ${\displaystyle X}$ is ${\displaystyle \rho (X)}$. A risk measure ${\displaystyle \rho :{\mathcal {L}}\to \mathbb {R} \cup \{+\infty \}}$ should have certain properties:

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