Before revision:  For the case of exponentially-distributed claims, we are able to improve the approximation arising from the diffusion, attaining a uniform O(n \mO\big( ^{ -1 } ) \big) rate of convergence \N . We also include two examples that illustrate our results.
After revision:  For the case of exponentially-distributed claims, we are able to improve the approximation arising from the diffusion, attaining a uniform O(n \mO\big( ^{ -1 } ) \big) rate of convergence for arbitrary k \in\N . We also include two examples that illustrate our results.