## Monotone and cash-invariant convex functions and hulls.(English)Zbl 1119.91051

Summary: This paper provides some useful results for convex risk measures. In fact, we consider convex functions on a locally convex vector space E which are monotone with respect to the preference relation implied by some convex cone and invariant with respect to some numeraire (‘cash’). As a main result, for any function $$f$$, we find the greatest closed convex monotone and cash-invariant function majorized by $$f$$. We then apply our results to some well-known risk measures and problems arising in connection with insurance regulation.

### MSC:

 91B30 Risk theory, insurance (MSC2010) 91B84 Economic time series analysis
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### References:

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