A Generalization of the Classical Risk Model

In this paper, we extend the classical risk process to the process, which is a spectrally negative L\'evy process minus a subordinator. Then some results of the ruin probability are derived in terms of properties of L\'evy process and some techniques from martingale theory. Finally, we derive some properties of hitting time and a Pollaczek-Khinchin type formula of the survival probability for a spectrally negative L\'evy process.