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On a class of approximative computation methods in the individual risk model. (English) Zbl 0805.62095
Summary: Exact calculations in the individual risk model are possible, but are very time consuming. Therefore, a number of recursive methods for approximate computation of the aggregate claims distribution and stop- loss premiums have been developed. In the present paper a general class of such approximation methods is considered, containing the higher order approximations suggested by P. S. Kornya [Trans. Soc. Actuar. 35, 823-836 (1983)], C. Hipp [ASTIN Bull. 16, No. 2, 89-100 (1986)], and the second author [ibid. 19, No. 1, 9-24 (1989); Scand. Actuarial J. 1988, No. 1/2, 61-68 (1988; Zbl 0664.62113)]. In this way, the treatment of the different methods is unified and extended to a more general setting. Some new theoretical error bounds are derived, giving a quantitative measure of the accuracy of the approximations.

62P05 Applications of statistics to actuarial sciences and financial mathematics
91B30 Risk theory, insurance (MSC2010)
65C99 Probabilistic methods, stochastic differential equations
Full Text: DOI
[1] De Pril, N., On the exact computation of the aggregate claims distribution in the individual life model, ASTIN bulletin, 16, 2, 109-112, (1986)
[2] De Pril, N., Improved approximations for the aggregate claims distribution of a life insurance portfolio, Scandinavian actuarial journal, 1988, 61-68, (1988) · Zbl 0664.62113
[3] De Pril, N., The aggregate claims distribution in the individual model with arbitrary positive claims, ASTIN bulletin, 19, 1, 9-24, (1989)
[4] De Pril, N.; Dhaene, J., Error bounds for compound Poisson approximations of the individual risk model, ASTIN bulletin, 22, 2, 135-148, (1992)
[5] Hipp, C., Improved approximations for the aggregate claims distribution in the individual model, ASTIN bulletin, 16, 2, 89-100, (1986)
[6] Hipp, C.; Michel, R., Risicotheorie: stochastische modelle und statistische methoden, (1990), Verlag Versicherungswirtschaft e.V Karlsruhe, Schriftenreihe Angewandte Versicherungsmathematik, Heft 24, Deutsche Gesellschaft für Versicherungsmathematik
[7] Kornya, P.S., Distribution of aggregate claims in the individual risk model, Transactions of the society of actuaries, 35, 823-836, (1983), Discussion: 837-858
[8] Kuon, S.; Reich, A.; Reimers, L., Panjer vs. kornya vs. de pril: A comparison from a practical point of view, ASTIN bulletin, 17, 2, 183-191, (1987)
[9] Panjer, H.H., Recursive evaluation of a family of compound distributions, ASTIN bulletin, 12, 1, 22-26, (1981)
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