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 |
Keywords:
constrained risk measures; convex duality; infimal convolution; insurance regulation; monotone and cash-invariant functions and hullsReferences:
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