Error bounds for the compound Poisson approximation. (English) Zbl 0541.62097

Summary: Explicit error bounds in terms of probabilities and stop-loss premiums are given for two kinds of compound Poisson approximations: the first concerns the difference between the individual and the collective model; the second is about the difference of the compound negative binomial and the compound Poisson distribution.


62P05 Applications of statistics to actuarial sciences and financial mathematics
Full Text: DOI


[1] Bowers, N.L.; Gerber, H.U.; Hickman, J.C.; Jones, D.A.; Nesbitt, C.J., Study note in risk theory, (1982), Society of Actuaries Chicago
[2] Brown, T.C., Poisson approximations and the definition of the Poisson process, The American mathematical monthly, 91, 2, 116-123, (1984) · Zbl 0552.60042
[3] Bühlmann, H.; Gagliardi, B.; Gerber, H.U.; Straub, E., Some inequalities for stop-loss premiums, The astin bulletin, 9, 75-83, (1977)
[4] Gerber, H.U., An introduction to mathematical risk theory, (), distributed by · Zbl 0431.62066
[5] Goovaerts, M.J.; de Vylder, F.; Haezendonck, J., Insurance premiums, (1984), North-Holland Amsterdam · Zbl 0532.62082
[6] Held, R.P., Zur rekursiven berechnung von stop loss-prämien für pensionskassen, Bulletin of the association of swiss actuaries, 1982, 1, 67-88, (1982) · Zbl 0479.62075
[7] Le Cam, L., An approximation theorem for the Poisson binomial distribution, Pacific J. math., 10, 1181-1197, (1960) · Zbl 0118.33601
[8] Seal, H.L., The Poisson process: its failure in risk theory, Insurance: mathematics & economics, 2, 4, 287-288, (1983)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.