Tempered stable distributions and finite variation Ornstein-Uhlenbeck processes

Relatore: Dott. Piergiacomo Sabino - Quantitative Risk Management (E.ON SE, Essen, Germany)

  • Data: 25 marzo 2021 dalle 16:00 alle 18:00

  • Luogo: Modalità telematica, mediante sistema di videoconferenza su piattaforma Microsoft Teams

Constructing Levy-driven Ornstein-Uhlenbeck processes is a task closely related to the notion of self-decomposability. In particular, their transition laws are linked to the properties of what will be hereafter called the a-remainder of their self-decomposable stationary laws. In the present study we fully characterize the Levy triplet of these a-remainders and we provide a general framework to deduce the transition laws of the finite variation Ornstein-Uhlenbeck processes associated with tempered stable distributions. We focus finally on the subclass of the exponentially-modulated tempered stable laws and we derive the algorithms for an exact generation of the skeleton of Ornstein-Uhlenbeck processes related to such distributions, with the further advantage of adopting a procedure computationally more efficient than those already available in the existing literature. The talk is based on a joint work with Prof. Nicola Cufaro Petroni.

Alberto Lanconelli