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In this paper we consider a compound Poisson risk model with regularlyvarying claim sizes. For this model in [1] an asymptotic formula for the finitetime ruin probability is provided when the time is scaled by the mean excessfunction. In this paper we derive the rate of convergence for this finite timeruin probability when the claims have a finite second moment.  [1] S. Asmussen and C. Kl\"uppelberg. Large deviations results forsubexponential tails, with applications to insurance risk. Stochastic Process.Appl., 64(1):103-125, 1996.

Second order corrections for the limits of normalized ruin times in the presence of heavy tails