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Let ${\bf X}({\bf t})=(X_1(t),X_2(s)), {\bf t}=(t,s)$ be a correlated two-dimensional Brownian motion and let $\mu_1,\mu_2>0$ be two constants. In this contribution, we derive the logarithmic asymptotics \[ \log P\Bigl( \sup_{t\ge 0} \Bigl( X_1(t) - \mu_1 t\Bigr)> u, \ \sup_{s\ge 0} \Bigl( X_2(s) - \mu_2 s\Bigr)> u \Bigr),\qquad u\to\infty. \]

Logarithmic Asymptotics for Probability of Component-Wise Ruin in a Two-Dimensional Brownian Model