Im Rahmen des Berufungsverfahren fuer eine
Professur aus Versicherungsmathematik
and der TU Wien finden folgende Vortraege statt:
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Freitag, 1. Maerz 2002, 13:15,
Freihaus HS 8 (Noebauer-Hoersaal), 2. Stock, gelber Bereich
http://www.wegweiser.ac.at/tuwien/hoersaal/F8.html
Wiedner Hauptstr. 8-10, 1040 Wien
Jeffrey Collamore (ETH-Zuerich)
Extremal Behavior of Multidimensional Risk Processes
In the classical ruin problem of collective risk theory,
an insurance company gains capital from premiums income and loses
capital as a result of claims; one then studies the probability that
the company's total capital ever falls below zero, i.e.,
P{S(t) < -m, for some t}, where S(t) is a positive-drift Levy process
and m is the company's initial capital.
In this talk I will discuss various generalizations of this
problem to higher dimensional settings. The first of these can be
described as follows: Let S(1),S(2),... be a sequence of random
vectors, corresponding e.g. to several capital factors, and consider
the probability that this sequence ever reaches some "forbidden
region" in d-dimensional Euclidean space. It will be shown that,
under quite general assumptions,
(*) (1/m) log P{S(n) ever hits mA} ~ -I(A)
for an appropriate "rate function" I(A). Some refinements,
describing e.g. the asymptotic distribution of the first passage
time, will also be given.
A second generalization which will be discussed is the case where
the increments of S(1),S(2),... are governed by a system of random
recurrence equations. Such recurrence equations are of considerable
applied interest and arise, among other places, in the study of GARCH
financial time series models and insurance models with stochastic
returns on the surplus capital. It will be shown that an asymptotic
estimate very similar to (*) can also be developed in this setting.
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Freitag, 1. Maerz 2002, 15:30
Freihaus HS 8 (Noebauer-Hoersaal), 2. Stock, gelber Bereich
http://www.wegweiser.ac.at/tuwien/hoersaal/F8.html
Wiedner Hauptstr. 8-10, 1040 Wien
Nicole Baeuerle (Universitaet Ulm)
Stochastische Steuerung in der Versicherungsmathematik
Das Problem der Bestimmung optimaler Dividendenaus-
schüttungs- und Rückversicherungsstrategien, das in Teilen
schon auf de Finetti (1957) zurückgeht, wurde in letzter
Zeit wieder intensiv untersucht. Da die ursprüngliche
Formulierung auf die optimale Steuerung eines stückweise
deterministischen Markov Prozesses führt - was sehr
schwierig ist - standen in letzter Zeit Diffusionsmodelle
im Vordergrund. In dem Vortrag wird auf beide
Formulierungen eingegangen und ein Zusammenhang
zwischen den Optimierungsproblemen hergestellt.
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