On some effects of dependencies on an insurer’s risk exposure, probability of ruin, and optimal premium loading

Abstract

AbstractWe study how the presence of dependencies between risks in a population of prospective insurance customers translates into risk exposure for an insurance company, depending on the company’s market share on the various risks. It turns out that the dependency structure in the insurer’s portfolio may differ significantly from the dependency structure of those risks in the general population, even when policyholders for different risks are selected independently. We obtain an upper bound for the difference between the ruin probability and its estimate based on the company’s portfolio marginal distributions. Under certain conditions, dependencies between risks in the portfolio of a company with small market shares are mild. We characterize the optimal loadings and market shares, assuming generic demand functions for the different risks.