Of happy and hapless regulators: the asymptotics of ruin

We employ a simple single-period ruin probability as a useful tool for studying various asymptotic effects associated with increasing the number of exposure units, n, covered by an insurer. These effects include: the law of large numbers, the roles of capital and underwriting profit loadings, and adverse selection. For a model with known parameters, we find the necessary and sufficient condition for the ruin probability to converge to zero, as well as sufficient conditions for the normal approximation to provide asymptotically accurate comparative statics with respect to n. For a model with parameter-estimation errors, we find that the normal approximation no longer holds in general, and that the necessary and sufficient condition for the ruin probability to approach zero becomes much more restrictive.