Itô calculus for Cramér-Lundberg model

Abstract

In insurance mathematics, specifically in risk theory, mainly functional analytic techniques are used. In this paper, we give an alternative approach to deriving some well-known, basic, but important results on the classical collective risk model. Applying techniques based on Itô's calculus, we derive an integro-differential equation for the Gerber-Shiu function, under the Cramér-Lundberg model.