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Daiane Rodrigues Dos Santos

Pontifícia Universidade Católica



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Cristiano Augusto Coelho Fernandes

Pontifícia Universidade Católica



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Joel Correa da Rosa

Rockefeller University



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489 – Time Series, Change Points, and Business Analytics

A Multivariate State Space Model for IBNR Reserve

Sponsor: Business and Economic Statistics Section
Keywords: IBNR, SUTSE, runoff triangle, state space models

Daiane Rodrigues Dos Santos

Pontifícia Universidade Católica

Cristiano Augusto Coelho Fernandes

Pontifícia 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.

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