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Experience Rating of ARIMA Processes by the Kalman Filter

Published online by Cambridge University Press:  29 August 2014

Jukka Rantala
Jukka Rantala*
Affiliation:
The Ministry of Social Affairs and Health, Helsinki
*
Ministry of Social Affairs and Health, Insurance Department, Bulevardi 28, SF-00120, Helsinki 12.
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Abstract

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This paper deals with experience rating of claims processes of ARIMA structures. By experience rating we mean that future premiums should be only a function of past values of the claims process. The main emphasis is on demonstrating the usefulness of the control-theoretical approach in the search for optimal rating rules. Optimality is here defined to mean as smooth a flow of premiums as possible when the variation in the accumulated profit is restricted to a certain amount. First it is shown how the underlying model in its simplest form can be transformed into the state-space form. Then the Kalman filter technique is used to find the optimal rules. Also a time delay in information is taken into account. The optimal rules are illustrated by examples.

Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 16 , Issue 1 , April 1986 , pp. 19 - 31
Copyright
Copyright © International Actuarial Association 1986

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