Weak Subordination of Multivariate Levy Processes

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).

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Zoom meeting link: https://unimelb.zoom.us/j/83757047993?pwd=a04zNitYZTRHdTZYdERkMmJYdDRWZz09

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