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A GAMMA MOVING AVERAGE PROCESS FOR MODELLING DEPENDENCE ACROSS DEVELOPMENT YEARS IN RUN-OFF TRIANGLES

Published online by Cambridge University Press:  04 November 2020

Luis E. Nieto-Barajas Open the ORCID record for Luis E. Nieto-Barajas [Opens in a new window]  and
Rodrigo S. Targino Open the ORCID record for Rodrigo S. Targino [Opens in a new window]
Luis E. Nieto-Barajas*
Affiliation:
Department of Statistics, Instituto Tecnológico Autónomo de México (ITAM), Mexico City, Mexico E-Mail: lnieto@itam.mx
Rodrigo S. Targino
Affiliation:
School of Applied Mathematics, Fundação Getulio Vargas (FGV), Rio de Janeiro, Brazil E-Mail: rodrigo.targino@fgv.br
*
E-Mail: lnieto@itam.mx
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Abstract

We propose a stochastic model for claims reserving that captures dependence along development years within a single triangle. This dependence is based on a gamma process with a moving average form of order $p \ge 0$ which is achieved through the use of poisson latent variables. We carry out Bayesian inference on model parameters and borrow strength across several triangles, coming from different lines of businesses or companies, through the use of hierarchical priors. We carry out a simulation study as well as a real data analysis. Results show that reserve estimates, for the real data set studied, are more accurate with our gamma dependence model as compared to the benchmark over-dispersed poisson that assumes independence.

Keywords

Claims reservinggamma processIncurred But Not Reportedlatent variablesmoving average processesC110C130C320C530
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 51 , Issue 1 , January 2021 , pp. 245 - 266
Copyright
© 2020 by Astin Bulletin. All rights reserved

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