Description: We find the necessary and sufficient conditions for fitting five given moments by a triatomic distribution. We consider three examples drawn from fire large spread, individual life medium spread and group life small spread insurance data, fit them with triatomics, and compute the ruin probabilities using well known formulas for discrete and for combination of exponentials claim amounts. We then compare our approximations with the exact values that appeared in the literature.

Description: Actuaries and other managers of risk identify factors in modeling insurance risks because [i] they feel that these factors may cause the outcome of a risk, or [ii] that the factors can be managed, thus allowing analysts a degree of control over the system risk. The purpose of this paper is to propose a framework for quantifying the relative importance of a source of risk. The intent is that, with a quantitative measure of relative importance, risk managers will be able to sharpen their intuition about the relative importance of risks and be better custodians of financial security systems. This paper proposes a measure of relative importance that has its roots in both the statistics and economics literatures. The measure is intuitively appealing when assessing the effectiveness of basic risk management techniques including risk exchange, pooling and financial risk management. The risk measure is also shown to be useful in multivariate situations where several factors affect a risk simultaneously. The paper illustrates this usefulness by considering a pool of policies that is subject to mortality, the risk of a disaster that is common to all policies, and to a common investment environment.

Description: In this paper, we propose measures of the risk that the value of the liabilities becomes larger than the value of the assets, and this especially for insurance companies. We study probabilities of mismatching and a degree of mismatching in unsegmented and multidimensional models of the balance, in which we stress the influence of interest rates on the active and passive side of the balance.