Timetable 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) (with J.Leitner)
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 measures.