De Vylder, F.; Marceau, E. The numerical solution of the Schmitter problems: Theory. (English) Zbl 0890.90037 Insur. Math. Econ. 19, No. 1, 1-18 (1996). Summary: The numerical solution of the Schmitter problems is based on a renewal equation in a discretization of the classical risk model, on a general optimization algorithm of functions on convex spaces, and on the introduction of directional derivatives in the risk model. Cited in 1 ReviewCited in 6 Documents MSC: 91B30 Risk theory, insurance (MSC2010) 62P05 Applications of statistics to actuarial sciences and financial mathematics Keywords:ruin probability; Schmitter problems; renewal equation; risk model; directional derivatives PDFBibTeX XMLCite \textit{F. De Vylder} and \textit{E. Marceau}, Insur. Math. Econ. 19, No. 1, 1--18 (1996; Zbl 0890.90037) Full Text: DOI References: [1] Brockelt, P.; Goovaerts, M.; Taylor, G., The Schmitter problem, ASTIN Bulletin, 21, h°.1, 129-132 (1991) [2] De Vylder, F. and M. Goovaerts. The bi-atomic uniform extremal solution of Schmitter’s problem. (submitted).; De Vylder, F. and M. Goovaerts. The bi-atomic uniform extremal solution of Schmitter’s problem. (submitted). · Zbl 0906.62107 [3] De Vylder, F., and M. Goovaerts. The solution of Schmitter’s simple problem: Numerical results. (forthcoming).; De Vylder, F., and M. Goovaerts. The solution of Schmitter’s simple problem: Numerical results. (forthcoming). · Zbl 0906.62108 [4] De Vylder, F., and E. Marceau. Schmitter’s problem: Existence and atomicity of the extremals. (submitted).; De Vylder, F., and E. Marceau. Schmitter’s problem: Existence and atomicity of the extremals. (submitted). · Zbl 0906.62107 [5] Gerber, H., Mathematical fun with the compound binomial Process, ASTIN Bulletin, 18, no. 2, 161-168 (1988) [6] Kaas, R., The Schmitter problem and a related problem: A partial solution, ASTIN Bulletin, 21, no. 1, 133-146 (1991) [7] Kaas, R.; Vanneste, M.; Goovaerts, H. J., Maximizing Compound Poisson Stop-Loss Premiums Numerically with given Mean and Variance (1992) [8] Robertson, A. P.; Robertson, W., Topological Vector Spaces (1964), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0123.30202 [9] Shiu, E. S.W., The probability of eventual ruin in the compound binomial model, ASTIN Bulletin, 19, no. 2, 179-190 (1989) 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.