For more information about this meeting, contact Manfred Denker, Anna Mazzucato, Alexei Novikov.
|Title:||On infinitely divisible semimartingales|
|Seminar:||Probability and Financial Mathematics Seminar|
|Speaker:||Jan Rosinski, University of Tennessee|
|Semimartingales play a fundamental role in stochastic analysis and mathematical finance. Concerning the latter, the discounted asset price process must be a semimartingale in order to preclude arbitrage opportunities. The question whether a given process with long memory, possible jumps and/or heavy tails is a semimartingale is also of importance in stochastic modeling, where such processes are used as a driving random motion for stochastic differential equations. We consider this question in the context of infinitely divisible processes, which include fractional processes, moving averages, and Ornstein-Uhlenbeck processes driven by stable, multi-stable, and tempered stable L\'evy processes, and their mixtures. We show that the problem when any such process is a semimartingale can often be reduced to a path property, when a certain associated infinitely divisible process is of finite variation. This gives the key to fully characterize the semimartingale property for many processes of interest, including processes mentioned above.
This talk is based on a joint work with Andreas Basse-O'Connor of Aarhus University.|
Room Reservation Information
|Date:||10 / 10 / 2014|
|Time:||03:35pm - 04:35pm|