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We outline the history of Risk Measures from the original formulation given by Artzner Delbaen Eber and Heath until the more recent research on quasiconvex Risk Measures. We therefore present some novel results on quasiconvex Risk Measures in the conditional setting, focusing on two different approaches: the vector space compared to the module approach. In particular the second one will guarantee a complete duality theory which is a key ingredient in the representation of risk preferences.
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