In this paper we consider a compound Poisson risk model with regularly varying claim sizes. For this model in [4] an asymptotic formula for the finite time ruin probability is provided when the time is scaled by the mean excess function. In this paper we derive the rate of convergence for this finite time ruin probability when the claims have a finite second moment.

Keywords: Second order asymptotic, Regular variation, Finite time ruin probability, Poisson process, Risk Process, Transient behavior, M/G/1 queue, Storage process.