CBI-time-changed Lévy processes

Orateur: Guillaume Szulda
Localisation: ,
Type: Séminaire de probabilités et statistiques
Site: UGE , 4B 125
Date de début: 09/11/2023 - 10:30
Date de fin: 09/11/2023 - 11:30

We introduce and study the class of CBI-time-changed Lévy processes (CBITCL), obtained by time-changing a Lévy process with respect to an integrated continuous-state branching process with immigration (CBI). We characterize CBITCL processes as solutions to a certain stochastic integral equation and relate them to affine stochastic volatility processes. We provide a complete analysis of the time of explosion of exponential moments of CBITCL processes and study their asymptotic behavior. In addition, we show that CBITCL processes are stable with respect to a suitable class of equivalent changes of measure. As illustrated by some examples, CBITCL processes are flexible and tractable processes with a significant potential for applications in finance.