  In this note we consider the two-dimensional risk model introduced in Avram
et al. \cite{APP08} with constant interest rate. We derive the
integral-differential equations of the Laplace transforms, and asymptotic
expressions for the finite time ruin probabilities with respect to the joint
ruin times $T_{\rm max}(u_1,u_2)$ and $T_{\rm min}(u_1,u_2)$ respectively.
