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Ordering of risks and ruin probabilities. (English) Zbl 0589.62089

The authors consider the classical model in risk theory, where the individual claim amounts are i.i.d. random variables and the claim number process is a homogeneous Poisson process. They give upper and lower bounds of the infinite-time ruin probability for different cases of information on the claim size distribution. In the following discussion of this paper G. C. Taylor calculates these bounds for a given numerical example and relates the results to some other investigations.
Reviewer: A.Reich

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
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References:

[1] Bowman, K. O.; Lam, H. K.; Shenton, L. R., Bounds for certain integrals, Journal of Computational and Applied Mathematics, 10, 4 (1984) · Zbl 0557.65012
[2] De Vylder, F.; Goovaerts, M., Bounds for classical ruin probabilities, Insurance: Mathematics and Economics, 3, 2, 121-131 (1984) · Zbl 0547.62068
[3] Goovaerts, M. J.; Kaas, R., Application of the problem of moments to derive bounds on integrals with integral constraints, Insurance: Mathematics and Economics, 4, 2, 99-111 (1985) · Zbl 0559.62086
[4] (Goovaerts, M.; De Vylder, F.; Haezendonck, J., Insurance Premiums (1983), North-Holland: North-Holland Amsterdam) · Zbl 0532.62082
[5] Taylor, G. C., Use of differential and integral inequalities to bound ruin and queueing probabilities, Scandinavian Actuarial Journal, 197-208 (1976) · Zbl 0338.60005
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