Broeckx, F.; Goovaerts, M.; de Vylder, F. Ordering of risks and ruin probabilities. (English) Zbl 0589.62089 Insur. Math. Econ. 5, 35-44 (1986). 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 Cited in 1 ReviewCited in 7 Documents MSC: 62P05 Applications of statistics to actuarial sciences and financial mathematics Keywords:independence and equidistribution assumptions; compound Poisson; process; risk theory; claim number process; homogeneous Poisson process; upper and lower bounds of the infinite-time ruin probability; claim size distribution; numerical example PDFBibTeX XMLCite \textit{F. Broeckx} et al., Insur. Math. Econ. 5, 35--44 (1986; Zbl 0589.62089) Full Text: DOI 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 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.