  We consider two bivariate models with two-way interactions in context of risk
and queueing theory. The two entities interact with each other by providing
assistance but otherwise evolve independently. We focus on certain random
quantities underlying the joint survival probability and the joint stationary
workload, and show that these admit stochastic decomposition. Each one can be
seen as an independent sum of respective quantities for the two models with
one-way interaction. Additionally, we discuss a rather general method of
establishing decompositions from a given kernel equation by identifying two
independent random variables from their difference, which may be useful for
other models. Finally, we point out that the same decomposition is true for
uncorrelated Brownian motion reflected to stay in an orthant, and it concerns
the face measures appearing in the basic adjoint relationship.
