  We consider two insurance companies with endowment processes given by
Brownian motions with drift. The firms can collaborate by transfer payments in
order to maximize the probability that none of them goes bankrupt. We show that
pushing maximally the company with less endowment is the optimal strategy for
the collaboration if the Brownian motions are correlated and the transfer rate
can exceed the drift rates. Moreover, we obtain an explicit formula for the
minimal ruin probability in case of perfectly positively correlated Brownian
motions where we also allow for different diffusion coefficients.
