Claims reserving with a stochastic vector projection

Luís Portugal, Athanasios A. Pantelous, Hirbod Assa

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Abstract

In the last three decades, a variety of stochastic reserving models have been proposed in the general insurance literature mainly using (or reproducing) the well-known Chain-Ladder claims-reserving estimates. In practice, when the data do not satisfy the Chain-Ladder assumptions, high prediction errors might occur. Thus, in this article, a combined methodology is proposed based on the stochastic vector projection method and uses the regression through the origin approach of Murphy, but with heteroscedastic errors instead, and different from those that used by Mack. Furthermore, the Mack distribution-free model appears to have higher prediction errors when compared with the proposed one, particularly, for data sets with increasing (regular) trends. Finally, three empirical examples with irregular and regular data sets illustrate the theoretical findings, and the concepts of best estimate and risk margin are reported.

Original languageEnglish
Pages (from-to)22-39
Number of pages18
JournalNorth American Actuarial Journal
Volume22
Issue number1
DOIs
Publication statusPublished - 14 Mar 2018
Externally publishedYes

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