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Stochastic modelling in experience rating. (Stochastische Modellierung in der Erfahrungstarifierung.) (German) Zbl 0781.62166
Summary: The idea of experience rating originated early in this century and has now become one of the basic principles of both actuarial practice and insurance mathematics. Probabilistic modelling of experience rating developed slowly and was subject to several changes. The present paper focuses on some selected aspects of model building in the past and in current research: The main steps in the development up to 1970, the genesis of the classical model around 1970, and variants of the classical model with regard to effects of perturbations of certain model assumptions.

62P05 Applications of statistics to actuarial sciences and financial mathematics
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[1] Bailey, A. L. (1945): A generalized theory of credibility. Proc. Casualty Act. Soc.32, 35–95.
[2] Bailey, A. L. (1950): Credibility precedures, Laplace’s generalization of Bayes’ rule and the combination of collateral knowledge with observed data. Proc. Casualty Act. Soc.37, 7–23.
[3] Bühlmann, H. (1967): Experience rating and credibility. ASTIN Bull.4, 199–207.
[4] Bühlmann, H. (1970): Mathematical Methods in Risk Theory. Berlin-Heidelberg-New York: Springer. · Zbl 0209.23302
[5] Bühlmann, H. (1975): Minimax credibility. In: Credibility – Theory and Applications (Berkeley 1974), 1–18. New York-London: Academic Press.
[6] De Vylder, F. (1976): Optimal semilinear credibility. Mitt. VSVM76, 27–40. · Zbl 0329.62077
[7] Eichenauer, J., Lehn, J., Rettig, S. (1988): A gamma-minimax result in credibility theory. Insurance Math. Econom.7, 49–57. · Zbl 0639.62089
[8] Gerber, U. (1980): Credibility for Esscher premiums. Mitt. VSVM80, 307–312. · Zbl 0446.62110
[9] Goovaerts, M. J., De Vylder, F., Haezendonck, J. (1984): Insurance Premiums. Amsterdam-New York: North-Holland. · Zbl 0532.62082
[10] Heilmann, W. R. (1987): Statistical decision theory and insurance ratemaking. In: Methods of Operations Research, Band 57, 559–581. Frankfurt: Athenäum. · Zbl 0617.62109
[11] Heilmann, W. R. (1988): Fundamentals of Risk Theory. Karlsruhe: Verlag Versicherungswirtschaft. · Zbl 0719.62112
[12] Heilmann, W. R. (1989): Decision theoretic foundations of credibility theory. Insurance Math. Econom.8, 77–95. · Zbl 0687.62087
[13] Hunt, G. A. (1966): Martingales et Processus de Markov. Paris: Dunod. · Zbl 0158.35802
[14] Lundberg, O. (1940): On Random Processes and Their Application to Sickness and Accident Statistics. Uppsala: Almquist and Wicksells (1964). · JFM 66.0678.01
[15] Marazzi, A. (1976): Minimax credibility. Mitt. VSVM76, 219–229 · Zbl 0341.62078
[16] Neveu, J. (1972): Martingales à Temps Discret. Paris: Masson.
[17] Schmidt, K. D. (1990): Convergence of Bayes and credibility premiums. ASTIN Bull.20, 167–172.
[18] Timpel, M. (1991): Erfahrungstarifierung bei gewichteter quadratischer Verlustfunktion. Diplomarbeit, Universität Mannheim.
[19] Whitney, A. W. (1918): The theory of experience rating. Proc. Casualty Act. Soc.4, 274–292.
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