Existence of a classical solution to the integro-differential equation arising in the Cramér--Lundberg non-life insurance model with proportional investment

This paper establishes that the survival probability in the non-life Cramér–Lundberg insurance model with proportional investment is a classical $C^2$-solution of the associated integro-differential equation under minimal moment conditions: it suffices that the claim size distribution is continuous and possesses a finite moment of some positive order.