  We re-visit the classical problem of optimal payment of dividends and
determine the degree to which the diffusion approximation serves as a valid
approximation of the classical risk model for this problem. Our results
parallel some of those in B\"auerle (2004), but we obtain sharper results
because we use a different technique for obtaining them. Specifically,
B\"auerle (2004) uses probabilistic techniques and relies on convergence in
distribution of the underlying processes. By contrast, we use comparison
results from the theory of differential equations, and these methods allow us
to determine the rate of convergence of the value functions in question.
