Tempered infinitely divisible distributions and processes - Michele Leonardo Bianchi; Svetlozar T. Rachev; Young Shin Kim; Frank J. Fabozzi (Karlsruher Institut für Technologie (KIT), Institut für Volkswirtschaftslehre (ECON), 2011)
In this paper, we construct the new class of tempered infinitely divisible (TID) distributions. Taking into account the tempered stable distribution class, as introduced by in the seminal work of Rosinsky , a modification of the tempering function allows one to obtain suitable properties. In particular, TID distributions may have exponential moments of any order and conserve all proper properties of the Rosinski setting. Furthermore, we prove that the modified tempered stable distribution is TID and give some further parametric example.
urn:nbn:de:swb:90-232379
Keywords: 330; stable distributions; tempered stable distributions; tempered infinitely divisible distributions; modified tempered stable distributions