Empirical kalman-Credibility
Tóm tắt
In a dynamic linear model the credibility estimator is given by the famous Kalman-filter algorithm. By inserting adequate parameter estimators one gets an empirical credibility estimator. Asymptotic optimality of the empirical credibility estimator is investigated and practicable parameter estimators are given for the most general situation.
Tài liệu tham khảo
Bühlmann, H. (1967): Experience rating and credibility. ASTIN Bulletin.
Bühlmann, H., Straub, E. (1970): Glaubwürdigkeit für Schadensätze. Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker.
De Jong, P.,Zehnwirth, B. (1983): Credibility theory and the Kalman-filter. Insurance: Mathematics & Economics.
Gerber, H. U., Jones, D. A. (1975): Credibility formulas of the updating type. Transactions of the society of actuaries.
Hachemeister, Ch. (1975): Credibility for regression models with application to trend. In Credibility: Theory and applications (ed. P. M. Kahn), New York.
Harvey, A. C, Fernandes, C. (1989): Time series models for insurance claims. Journal of institute of actuaries
Ledolter, J., Klugman, S., Lee, C. S. (1991): Credibility models with time-varying trend component. ASTIN Bulletin.
Kremer, E. (1994): The linear growth credibility model. Scandinavian Actuarial Journal.
Kremer, E. (1985): Einführung in die Versicherungsmathematik. Vandenhoek & Ruprecht, Göttingen & Zürich.
Kremer, E. (1988 a): Box-Jenkins Credibility. Blätter der deutschen Gesellschaft für Versicherungsmathematik. Correction notes in October 1991, April 1992.
Kremer, E. (1988 b): General exponential smoothing credibility. Bulletin of the Belgian Actuarial Association.
Mangold, K. P. (1987): Rekursive Schätzverfahren in der Kreditbilitätstheorie. Blätter der deutschen Gesellschaft für Versicherungsmathematik.
Mehra, R. K. (1975): Credibility theory and Kalman-filtering with extensions. International Institute for applied systems analysis. Laxenburg, Austria.
Mowbray, A. H. (1914): How extensive a payroll exposure is necessary to give a dependable pure premium. Proceedings of the Casualty Actuarial Society.
Neuhaus, W. (1987): Early Warning. Scandinavian Actuarial Journal.
Norberg, R. (1980): Empirical Bayes credibility. Scandinavian Actuarial Journal.
Norberg, R. (1982): On optimal parameter estimation. Insurance: Mathematics & Economics.
Norberg, R. (1986): Hierarchical credibility: Analysis of a random effect linear model with nested classification. Scandinavian Actuarial Journal.
Rantala, J. (1983): Experience rating of claims processes with stochastic trends. ASTIN colloquium at Lindau.
Sundt, B. (1980): A multi-level hierarchical credibility model. Scandinavian Actuarial Journal.
Sundt, B. (1981): Recursive credibility estimation. Scandinavian Actuarial Journal.
Sundt, B. (1983): Finite credibility formulae in evolutionary models. Scandinavian Actuarial Journal.
Taylor, G. C. (1979): Credibility analysis of a general hierarchical model. Scandinavian Actuarial Journal.
Witney, A. W. (1918): The theory of experience rating. Proceedings of the Casualty Actuarial Society.
Zehnwirth, B. (1985): A linear filtering approach to recursive credibility estimation. ASTIN Bulletin.
Zehnwirth, B. (1986): A generalisation of the Kalman-filter based on either Gauss-Markov or linear Bayes theories. Journal of the American Statistical Association.