Mon, 16 Aug 2004 15:10:23 +0200
Tuesdays and Thursdays, 16:30-18:00,
TU FH, Turm A, 6. Stock, Seminarraum 107.
Tu, 17.08.2004 Pavel Grigoriev
Representation of "dilatation monotonous" or "co-monotonic additive"
risk measures (capacities)
We study the special class of coherent risk measures which satisfy an
additional property called "dilatation monotonicity" (monotonicity with
respect to taking conditional expectations over arbitrary sub sigma
algebras). This property appears to be natural for at least 2 reasons:
First, the conditioned random gain is "more determined" than the original
one and so it should be less risky; second, all risk measures which are
consistent with respect to utility maximization over all utility functions
are dilatation monotonous.
In particular, we proved that the dilatation monotonicity is equivalent to
so-called "co-monotonic additivity". In the case of atomless probability
space the dilatation monotonicity implies the risk measure is also law
invariant. Among the other results we characterized the extreme points of
the set of scenario probabilities for dilatation monotonous coherent risk