José Luis Pérez Garmendia (CIMAT): Fluctuation theory for spectrally negative Lévy processes killed by an additive functional and applications to the penalization problem

In this talk, we solve exit problems for spectrally negative Lévy processes that are exponentially killed with a killing intensity depending on an additive functional of the process. We also study the associated resolvents. All identities are expressed in terms of new generalizations of scale functions. Our results extend those for omega-killed spectrally negative Lévy processes obtained by Palmowski and Li. Finally, we apply these findings to derive penalization results for spectrally negative Lévy processes with clocks driven by additive functionals. This is joint work with Kei Noba, Kouji Yano, and Kohki Ibba.