| In this dissertation, we work with some asymptotic results regarding the probability of insolvency and the size of a market (i.e. optimal number of reinsurers for a given number or primary insurers). These results are of interest to both insurance regulators and policymakers as a way to develop a more efficient risk management surveillance system.; We begin by analyzing the ability of a regulator to monitor the solvency of an insurer with a growing number of exposure units in the context of a single-period ruin probability model. Using this model, we find both the necessary and sufficient condition for the ruin probability to converge to zero as the number of exposure units increases without bound, and the sufficient conditions for the normal approximation to provide asymptotically accurate comparative statics with respect to the number of exposures. Then, turning to a closer examination of comparative statics, we present a mathematical formulation for insurers and regulators to study the asymptotic relationships among the law of large numbers, the insurer's capital supply, the insurer's underwriting profit loading, and adverse selection.; Subsequently, we consider how the introduction of parameter uncertainty in the single-period ruin model affects the ability of regulators to monitor the probability of ruin. For this model 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.; Later, we test empirically the "square-root" rule model of Powers and Shubik (2005). Those authors have shown that the optimal number of reinsurers in a market is given asymptotically by the square root of the total number of primary insurers. To test this model we apply cross-sectional regressions with the number of reinsurers and primary insurers from several countries as the individual points. In addition to finding evidence consistent with the square-root rule, we find that the number of reinsurers in a market may be associated with an individuals' risk aversion. We then investigate the relationship between property-liability insurers' underwriting results and this coefficient of risk aversion, the so called "price of risk". |
