Minimum Distance Estimation of Loss Distributions

Loss distributions have a number of uses in the pricing and reserving of casualty insurance. Many authors have recommended maximum likelihood for the estimation of the parameters. It has the advantages of asymptotic optimality (in the sense of mean square error) and applicability (the likelihood function can always be written). Also, it is possible to estimate the variance of the estimate, a useful tool in assessing the accuracy of any results. The only disadvantage of maximum likelihood is that the objective function does not relate to the actuarial problem being investigated. Minimum distance estimates can be tailored to reflect the goals of the analysis and, as such, should give more appropriate answers. The purpose of this paper is to demonstrate that these estimates share the second and third desirable qualities with maximum likelihood. Reinsurance Research - Loss Distributions, Size of