CS11: Community Detection on Random Network Models

Organizer: Sandro Gallo (UFSCar and LAAS-CNRS)

Optimality of a barrier strategy in a spectrally negative Lévy model with a level-dependent intensity of bankruptcy

Jean-Francois Renaud

The stochastic control problem concerned with the maximization of dividend payments in a model based on a spectrally negative Lévy process (SNLP) has attracted a lot of research interest since the papers of Avram, Palmowski & Pistorius (2007) and Loeffen (2008). In that problem, a dividend strategy is said to be optimal if it maximises the expected present value of dividend payments made up to the time of ruin, which is a standard first-passage time below zero. In this talk, I will consider a version of this stochastic control problem in which the (controlled) process is allowed to spend time under zero, but is then subject to a level-dependent intensity of bankruptcy. In a joint paper with Dante Mata (UQAM & CRM), we were able to prove that there exists a barrier strategy that is optimal for this control problem, under a mild assumption on the Lévy measure.