  We consider a bivariate Cramer-Lundberg-type risk reserve process with the
special feature that each insurance company agrees to cover the deficit of the
other. It is assumed that the capital transfers between the companies are
instantaneous and incur a certain proportional cost, and that ruin occurs when
neither company can cover the deficit of the other. We study the survival
probability as a function of initial capitals and express its bivariate
transform through two univariate boundary transforms, where one of the initial
capitals is fixed at 0. We identify these boundary transforms in the case when
claims arriving at each company form two independent processes. The expressions
are in terms of Wiener-Hopf factors associated to two auxiliary compound
Poisson processes. The case of non-mutual (reinsurance) agreement is also
considered.
