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Experience Rating of ARIMA Processes by the Kalman Filter

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  • Rantala, Jukka

Abstract

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.

Suggested Citation

  • Rantala, Jukka, 1986. "Experience Rating of ARIMA Processes by the Kalman Filter," ASTIN Bulletin, Cambridge University Press, vol. 16(1), pages 19-31, April.
    • Handle: RePEc:cup:astinb:v:16:y:1986:i:01:p:19-31_00
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    Cited by:

    1. Yang, Lin & Pantelous, Athanasios A. & Assa, Hirbod, 2016. "Robust Stability, Stabilisation And H-Infinity Control For Premium-Reserve Models In A Markovian Regime Switching Discrete-Time Framework," ASTIN Bulletin, Cambridge University Press, vol. 46(3), pages 747-778, September.

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