A Multivariate State Space Model for IBNR Reserve

• Activity Number: 489
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Daiane Rodrigues Dos Santos* and Cristiano Augusto Coelho Fernandes and Joel Correia Da Rosa
• Companies: Pontifícia Universidade Católica and Pontifícia Universidade Católica and Rockefeller University
• Keywords: IBNR ; multivariate state space models ; unobserved components

Abstract

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.