We discuss two issues about risk measures: we first point out an alternative interpretation of the penalty function in the dual representation of a risk measure; then we analyze the continuity properties of comonotone convex risk measures. In particular, due to the loss of convexity, local and global continuity are no more equivalent and many implications true for convex risk measures do not hold any more.
Frittelli, M., ROSAZZA GIANIN, E. (2011). On the penalty function and on continuity properties of risk measures. INTERNATIONAL JOURNAL OF THEORETICAL AND APPLIED FINANCE, 14(1), 163-185 [10.1142/S0219024911006309].
On the penalty function and on continuity properties of risk measures
ROSAZZA GIANIN, EMANUELA
2011
Abstract
We discuss two issues about risk measures: we first point out an alternative interpretation of the penalty function in the dual representation of a risk measure; then we analyze the continuity properties of comonotone convex risk measures. In particular, due to the loss of convexity, local and global continuity are no more equivalent and many implications true for convex risk measures do not hold any more.
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