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A MIXTURE MODEL FOR PAYMENTS AND PAYMENT NUMBERS IN CLAIMS RESERVING

Published online by Cambridge University Press:  17 October 2016

Patrizia Gigante ,
Liviana Picech  and
Luciano Sigalotti
Patrizia Gigante
Affiliation:
Dipartimento di Scienze Economiche, Aziendali, Matematiche e Statistiche ‘B. de Finetti’, University of Trieste, Piazzale Europa 1, 34127 Trieste, Italy, E-Mail: [email protected]
Liviana Picech*
Affiliation:
Dipartimento di Scienze Economiche, Aziendali, Matematiche e Statistiche ‘B. de Finetti’, University of Trieste, Piazzale Europa 1, 34127 Trieste, Italy
Luciano Sigalotti
Affiliation:
Dipartimento di Scienze Economiche e Statistiche, University of Udine, Via Tomadini 30, 33100 Udine, Italy, E-Mail: [email protected]
*
E-Mail: [email protected]
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Abstract

We consider a Tweedie's compound Poisson regression model with fixed and random effects, to describe the payment numbers and the incremental payments, jointly, in claims reserving. The parameter estimates are obtained within the framework of hierarchical generalized linear models, by applying the h-likelihood approach. Regression structures are allowed for the means and also for the dispersions. Predictions and prediction errors of the claims reserves are evaluated. Through the parameters of the distributions of the random effects, some external information (e.g. a development pattern of industry wide-data) can be incorporated into the model. A numerical example shows the impact of external data on the reserve and prediction error evaluations.

Keywords

Claims reservingTweedie's compound Poisson modelconditional mean square error of predictionhierarchical generalized linear modelsh-likelihood
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 48 , Issue 1 , January 2018 , pp. 25 - 53
Copyright
Copyright © Astin Bulletin 2016 

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