Preprint : Ruin probability for the insurer-reinsurer model for exponential claims

In this paper we consider a two-dimensional risk process in which the companies split each claim in a fixed proportion which is also reflected in the collected premium. This serves as a classical framework of a proportional reinsurance contract. For the analyzed model, we derive a joint infinite-time ruin probability formula for claims given by an exponential distribution. To this end we apply a change of measure technique. For exponentially distributed claims we obtain a formula which simplifies Theorem 2 from Avram, Palmowski and Pistorius [Insurance: Mathematics and Economics 42 (2008) 227].