  The present work concerns the finite-time ruin probabilities for several
bidimensional risk models with constant interest force and correlated Brownian
motions.} Under the condition that the two Brownian motions $\{B_1(t), t\ge
0\}$ and $\{B_2(t), t\ge 0\}$ are correlated, we establish new results for the
finite-time ruin probabilities. \textcolor{blue} {Our research has enriched the
development of the ruin theory with heavy tails in unidimensional risk models
and the dependence theory of stochastic processes.
