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Linear Estimation and Credibility in Continuous Time1

Published online by Cambridge University Press:  29 August 2014

Ragnar Norberg
Ragnar Norberg*
Affiliation:
University of Copenhagen
*
Laboratory of Actuarial Mathematics, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark.
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Abstract

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The theory of linear filtering of stochastic processes provides continuous time analogues of finite-dimensional linear Bayes estimators known to actuaries as credibility methods. In the present paper a selfcontained theory is built for processes of bounded variation, which are of particular relevance to insurance. Two methods for constructing the optimal estimator and its mean squared error are deviced. Explicit solutions are obtained in a continuous time variation of Hachemeister's regression model and in a homogeneous doubly stochastic generalized Poisson process. The traditional discrete time set-up is compared to the one with continuous time, and some merits of the latter are pointed out.

Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 22 , Issue 2 , November 1992 , pp. 149 - 165
Copyright
Copyright © International Actuarial Association 1992

Footnotes

1

Presented to the XXII ASTIN Colloquium, Montreux, Sept. 90.

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