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Einladung_mit_Abstract_20060606
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Fulltext:
UniversitÂät Bremen
Fachbereich Mathematik Sommersemester 2006
Einladung zum
MATHEMATISCHEN KOLLOQUIUM
Am Dienstag, dem 6. Juni 2006
spricht
Prof. Dr. Ludger RÂüschendorf
UniversitÂät Freiburg
Âüber
Risk measures for portfolio vectors
The main purpose to study risk measures for portfolio vectors X = (X1, . . . , Xd) is to measure
not only the risk of the marginals Xi separately but to measure the joint risk of X caused by
the variation of the components and their possible dependence.
Thus an important property of risk measures for portfolio vectors is consistency with respect
to various classes of convex and dependence orderings. From this perspective we introduce
and study convex risk measures for portfolio vectors deï¬ned axiomatically. In particular we
characterize law invariant convex risk measures. We further introduce two natural and easy to
interprete and calculate classes of examples of risk measures for portï¬lio vectors and investigate
their consistency properties.
In the second part we consider an application of risk measures to the optimal risk allocation
problem. The optimal risk allocation problem or equivalently the problem of risk sharing is
the problem to allocate a risk in an optimal way to n traders endowed with risk measures
1, . . . , n. This problem has a long history in mathematical economics and insurance. We show
that the optimal risk allocation problem is well deï¬ned only under an equilibrium condition. This
condition can be characterized by the existence of a common scenario measure. We formulate a
meaningful modiï¬cation of the optimal risk allocation problem also for markets without assuming
the equilibrium condition and characterize otpimal solutions. The basic idea is to restrict the
class of admissible allocations in a proper way.
Der Vortrag ï¬ndet statt um 17 Uhr c.t. im Raum 7260, 7. Ebene des
Mehrzweckhochhauses (MZH) der UniversitÂät Bremen, Bibliothekstr.
Zuvor gibt es Kaffee/Tee und GebÂäck im Raum 7140.
Alle Interessierten sind herzlich eingeladen.
Ulrich Krause als Kolloquiumsbeauftragter.
Invitation_with_Abstract_20060606 Einladung_mit_Abstract_20060606
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