Im Rahmen des Berufungsverfahren fuer eine Professur aus Versicherungsmathematik and der TU Wien finden folgende Vortraege statt: =================================================================== 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. =================================================================== 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. ===================================================================