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Through an axiomatic approach, Artzner et al.  defined an important class of risk measures known as the coherent risk measure (CRM) and they shown that VaR.
A coherent risk measure equals the maximum expected loss under several different probability measures, and these measures are analogous to “ populations” or “ ...
2. Coherent measures of risk. The theory of coherent risk measures was initiated by Artzner et al., 1997, Artzner et al., 1999 and developed further by Bertsimas et al. (2000), Delbaen (2000), Kusuoka (2001), Acerbi (2002), Fritelli and Rosazza Gianin (2002), Acerbi …
Through an axiomatic approach, Artzner et al.  defined an important class of risk measures known as the coherent risk measure (CRM) and they shown that VaR. Note that V0 - V is a measure of our loss, not our gain ... hence it measures "risk". For example, Figure 3 is a sample cumulative distribution of portfolios, M months ...
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