Abstract: Consideres a diffusion perturbed Erlang(2) risk model with a constant dividend barrier, discusses the integro－differential equation with certain boundary conditions for M(x,y;b), the integral equation for M(x,y;b), obtaines the conditions under which M(x,y;b) is continuously differentiable through the integral equation.

Key words: Erlang(2) risk model, diffusion, dividend barrier, integro－differential equation, boundary condition