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Filipović, Damir; Kupper, Michael

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

Insur. Math. Econ. 41, No. 1, 1-16 (2007).
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.

Cited in 21 Documents

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 hulls
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\textit{D. Filipović} and \textit{M. Kupper}, Insur. Math. Econ. 41, No. 1, 1--16 (2007; Zbl 1119.91051)
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