Premium
A state space model for rub‐off triangles
Author(s) -
Alpuim Teresa,
Ribeiro Isabel
Publication year - 2003
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.484
Subject(s) - state space , variance (accounting) , kalman filter , mathematics , state space representation , space (punctuation) , statistics , mean squared error , column (typography) , order (exchange) , distribution (mathematics) , state (computer science) , econometrics , computer science , economics , algorithm , geometry , finance , mathematical analysis , accounting , connection (principal bundle) , operating system
In this paper we suggest a distribution‐free state space model to be used with the Kalman filter in run‐off triangles. It works with original incremental amounts and relates the triangle with a column of observed values, which can be chosen in order to describe better the risk volume in each year. On the traditional application of run‐off triangles (the paid claims run‐off), this model relates the amount paid j years after the accident year with a column of observed values, that can be the claims paid on the first year, the number of claims, premiums, number of risks, etc. Two advantages of this model are the perfect split between observed values and random variables and the capacity to incorporate the changes in the speed of the company's reality into the model and in its projections. Particular care is taken on the evaluation of the final forecast mean square error as well as on the estimation of the model parameters, specially the error variances. Also, two sets of claims data are analysed. In comparison with other methods, namely, the chain ladder, the analysis of variance, the Hoerl curves and the state space modelling with the chain ladder linear model, the proposed model gave a final reserve with a mean square error within the smallest. Copyright © 2003 John Wiley & Sons, Ltd.