Plenary I: Two-barrier problems in applied probability

Søren Asmussen 　  Aarhus University

Abstract

We consider a stochastic process X between two barriers 0 and K who may be absorbing or reflecting. The netput process is typically a L'evy process or a random walk, possibly with Markov-modulation. The absorbing case occurs in the classical gambler's ruin problem and we discuss some extended situations where the absorbtion probabilities can be computed. In the reflecting case, we look at the stationary distribution, the overflow rate at the upper barrier and characteristics of the first overflow time. Examples include Markov-modulated queues, mnay-server queues and barrier options.

Brief Biography

Søren Asmussen  was born in 1946 Studies in mathematics and mathematical statistics in Copenhagen, PhD 1977. Currently (since Feb 1, 2003, by "kaldelse")professor in applied probability at Aarhus University. Earlier employments in Copenhagen 1976-86, Aalborg 87-95 (as research professor 1990-95) and in Lund as professor 1995-2003. Longer visiting appointments/sabbaticals at Cornell University 1975,The Australian National University 1980-81, Stanford University 1986,University of California, Santa Barbara 1988, Chalmers Institute of Technology (jubileee professor) 1989, Columbia University 1998,Aarhus University 1999, University of Rome La Sapienza 2002. Research in applied probability,in particular branching processes, queueing theory, insurance risk,simulation. Three books, about 105 research papers (57 co-authors), about 15 papers in conference proceedings. Senior editor of the Annals of Applied Probability 00-02; earlier appointments as associate editor of Stochastic Models, Stochastic Processes and Their Applications, Queueing systems, Bernoulli. Marcel F. Neuts Applied Probability Prize 1999. INFORMS Simulation Outstanding Publication Award 2002. Supervisor of 5 finished PhD dissertations, 2 in progress, 10 M.Sc. dissertations 1984-2002.