  In this paper we study the joint ruin problem for two insurance companies
that divide between them both claims and premia in some specified proportions
(modeling two branches of the same insurance company or an insurance and
re-insurance company). Modeling the risk processes of the insurance companies
by Cram\'{e}r-Lundberg processes we obtain the Laplace transform in space of
the probability that either of the insurance companies is ruined in finite
time. Subsequently, for exponentially distributed claims, we derive an explicit
analytical expression for this joint ruin probability by explicitly inverting
this Laplace transform. We also provide a characterization of the Laplace
transform of the joint ruin time.
