Estimating IBNR Claims Reserves for General Insurance Using Archimedean Copulas

Abstract

Claims reserving for general insurance business has developed significantly over the recent past. There has always been a slight mystery in short-term insurance contracts of how to go about reserving for claims, which have not yet come in, and are still in some sense of figment of the future. Insurance claims variables are non-normally distributed and therefore a measure that will capture the dependence among the variables better than the usual correlation is employed. One such method is the use of copulas. The object of this paper, therefore, is to use the Archimedean copula, Clayton copula and Frank copula to estimate outstanding incurred but not reported (IBNR) claim reserves. A comparison of the estimates of outstanding claim reserves obtained from different Archimedean copulas is also presented.