Weak Subordination of Multivariate Levy Processes
Date: 4 August 2022, Thursday
Time: 5pm AEST
Statistics and Stochastic colloquium (part of the Colloquium Series of the Department of Mathematics and Statistics) at La Trobe University jointly organized with the Probability Victoria Seminar.
Contact the organizers: Kostya Borovkov kostya.borovkov@gmail.com, Andriy Olenko a.olenko@latrobe.edu.au
Speaker: Dr Boris Buchmann, ANU
Abstract: Subordination is the operation which evaluates a Levy process at a subordinator, giving rise to a pathwise construction of a "time-changed" process. Originating with Bochner in the context of probability semigroups, subordination was applied by Madan and Seneta to create the variance gamma process, which is prominently used in financial modelling. However, unless the subordinate has independent components or the subordinator has indistinguishable components, subordination may not produce a Levy process.
We introduce a new operation known as weak subordination that always produces a Levy process by assigning the distribution of the subordinate conditional on the value of the subordinator, and matches traditional subordination in law in the cases above. Weak subordination is applied to extend the class of variance generalised gamma convolutions and to construct the weak variance-alpha-gamma process. The latter process exhibits a wider range of dependence than using traditional subordination.
Joint work with Kevin W Lu (UW), Dilip B Madan (UM), Marcus Michaelsen (UHH), Adam Nie (NTU), Alex Szimayer (UHH).
Zoom meeting link:
https://unimelb.zoom.us/j/83757047993?pwd=a04zNitYZTRHdTZYdERkMmJYdDRWZz09
(if the link doesn't work when you click it -- please copy & paste it into the address bar in your browser).
Password: 916563 (just in case)
A PDF file with the talk slides might become available for downloading from our seminar Webpage at https://probvic.wordpress.com/pvseminar/ prior to the talk (the above Zoom is being posted there)
