In the classical risk model with initial capital u, let τ(u) be the time of ruin, X
+(u) be the risk reserve just before ruin, and Y
+(u) be the deficit at ruin. Gerber and Shiu (1998) defined the function m
δ(u) =E[e−δ τ(u)
+(u)) 1 (τ(u) < ∞)], where δ ≥ 0 can be interpreted as a force of interest and w(r,s) as a penalty function, meaning that m
δ(u) is the expected discounted penalty payable at ruin. This function is known to satisfy a defective renewal equation, but easy explicit formulae for m
δ(u) are only available for certain special cases for the claim size distribution. Approximations thus arise by approximating the desired m
δ(u) by that associated with one of these special cases. In this paper a functional approach is taken, giving rise to first-order correction terms for the above approximations.