Abtract:

Subordination is the operation that evaluates a Lévy process at a subordinator, giving rise to a pathwise construction of a “time-changed” process. In probability semigroups, subordination was applied to create the variance gamma process, which is prominently used in financial modelling. However, subordination may not produce a Lévy process unless the subordinate has independent components or indistinguishable components. A new operation known as weak subordination is introduced that always produces a Lévy process by assigning the distribution of the subordinate conditional on the value of the subordinator, matching 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, which exhibits a wider range of dependence than traditional subordination. This is joint work with Ross Maller, Kevin Lu, Dilip Madan, and Adam Nie.

This talk is free and open to all interested participants.

Location: Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Room 1101 – F435.