In the last ten years we have been facing the development on new approaches in Risk Measurement. The Coherent, Expectation Bounded, Convex, Consistent, etc. Risk Measures have been introduced and deeply studied, but there are many open problems that will have to be addressed in forthcoming research. The present paper attempts to summarize the achieved findings and the "State of the Art", as well as their relationships with other Mathematical Fields, with special focus on other usual topics of Mathematical Finance.
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