Insurance Premiums and Default Risk in Mutual Insurance

Two types of default risk are discussed in the article: The traditional “probability of ruin” (insurer being unable to meet his obligations) and a “perceived probability of ruin” (the probability of the insured being affected by ruin). The explicit relationship between these probabilities on the actuarial loading factors of a mutual insurer were developed. The explicit mathematical formulae obtained for these complex relationships were followed also by numerical results. A second concept presented in the paper is related to the idea of actuarially fair premiums. It is shown that the premium must also be a function of the payments of the other insured as well as their claim distributions, reflecting thereby the simultaneity and mutual dependence of the insured.