  We investigate an insurance risk model that consists of two reserves which
receive income at fixed rates. Claims are being requested at random epochs from
each reserve and the interclaim times are generally distributed. The two
reserves are coupled in the sense that at a claim arrival epoch, claims are
being requested from both reserves and the amounts requested are correlated. In
addition, the claim amounts are correlated with the time elapsed since the
previous claim arrival. We focus on the probability that this bivariate reserve
process survives indefinitely. The infinite- horizon survival problem is shown
to be related to the problem of determining the equilibrium distribution of a
random walk with vector-valued increments with reflecting boundary. This
reflected random walk is actually the waiting time process in a queueing system
dual to the bivariate ruin process. Under assumptions on the arrival process
and the claim amounts, and using Wiener-Hopf factor- ization with one
parameter, we explicitly determine the Laplace-Stieltjes transform of the
survival function, c.q., the two-dimensional equilibrium waiting time
distribution. Finally, the bivariate transforms are evaluated for some
examples, including for proportional reinsurance, and the bivariate ruin
functions are numerically calculated using an efficient inversion scheme.
