On joint ruin probabilities of a two-dimensional risk model with constant interest rate

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 $T_{\mathrm{m}\mathrm{a}\mathrm{x}}(u_1,u_2)$ and $T_{\mathrm{m}\mathrm{i}\mathrm{n}}(u_1,u_2)$ respectively.