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In this article we review the main approaches extensively investigated for claims reserving in general insurance.We first introduce the models underlying the most-known Chain Ladder method and Bornhuetter-Ferguson method.Then we discuss their Bayesian versions,Generalized limear models for claims reserving and the bootstrap approaches to evaluating the variabilty of predicted/estimated reserves are reviewed also.In addition.we conclude the paper by introducing the multivariate version for claims reserving methods.