  We consider a two-dimensional ruin problem where the surplus process of
business lines is modelled by a two-dimensional correlated Brownian motion with
drift. We study the ruin function $P(u)$ for the component-wise ruin (that is
both business lines are ruined in an infinite-time horizon), where $u$ is the
same initial capital for each line. We measure the goodness of the business by
analysing the adjustment coefficient, that is the limit of $-\ln P(u)/u$ as $u$
tends to infinity, which depends essentially on the correlation $\rho$ of the
two surplus processes. In order to work out the adjustment coefficient we solve
a two-layer optimization problem.
