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International Journal for Uncertainty Quantification
IF: 0.967 5-Year IF: 1.301 SJR: 0.531 SNIP: 0.8 CiteScore™: 1.52

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.v2.i1.40
pages 39-51

A NON-PARAMETRIC METHOD FOR INCURRED BUT NOT REPORTED CLAIM RESERVE ESTIMATION

Helio Lopes
Departamento de Matematica, Pontiftcia Universidade Catolica do Rio de Janeiro, Rio de Janeiro, Brazil
Jocelia Barcellos
Departamento de Matematica, Pontiftcia Universidade Catolica do Rio de Janeiro, Rio de Janeiro, Brazil
Jessica Kubrusly
Instituto de Matematica e Estatistica, Universidade Federal Fluminense, Niteroi, Rio de Janeiro, Brazil
Cristiano Fernandes
Departamento de Engenharia Eletrica, Pontificia Universidade Catolica do Rio de Janeiro, Rio de Janeiro, Brazil

ABSTRACT

The number and cost of claims that will arise from each policy of an insurance company′s portfolio are unknown. In fact, there is a high degree of uncertainty on how much will ultimately be the cost of claims, not only during the period of inception but also after the contract termination, since there might be future, not yet reported, losses associated with past claims. Therefore, in practice, insurance companies have to protect themselves against the possibility of this ultimate cost by creating an additional reserve known as the incurred but not reported (IBNR) reserve. This work introduces new non-parametric models to IBNR estimation based on kernel methods; namely, support vector regression and Gaussian process regression. These are used to learn certain types of nonlinear structures present in claims data using the residuals produced by a benchmark IBNR estimation model, Mack′s chain ladder. The proposed models are then compared to Mack′s model using real data examples. Our results show that the three new proposed models are competitive when compared to Mack′s benchmark model: they may produce the closest predictions of IBNR and also more accurate estimates, given that the variance for the reserve estimation, obtained through the bootstrap technique, is usually smaller than the one given by Mack′s model.