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489 – Time Series, Change Points, and Business Analytics
A Multivariate State Space Model for IBNR Reserve
Daiane Rodrigues Dos Santos
PontifÃcia Universidade Católica
Cristiano Augusto Coelho Fernandes
PontifÃcia Universidade Católica
Joel Correa da Rosa
Rockefeller University
In this article we propose a multivariate extension of Atherino's model (2010), in which insurance claims are organized as "time series" by stacking the columns of the runoff triangle in which the IBNR (incurred but not reported) claims are grouped. Such "time series" will display periodic movements which can be duly captured by a "seasonal" component. In order to do so the structural time series model of Harvey (1989) is used. Our multivariate extension uses a SUTSE (seemingly unrelated time series equations) structure, in which each IBNR series has its own "seasonal" but the shocks are correlated. This approach provides a more parsimonious description of correlated IBNR reserves. We apply this model to a bivariate claim series of the Brazilian car insurance market. Our results show that the proposed model presents better results than its univariate counterpart.