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Classical numerical ruin probabilities. (English) Zbl 0880.62108
Summary: Finite and infinite-time classical ruin probabilities can be approximated in H. U. Gerber’s [Insur. Math. Econ. 7, No. 1, 15-23 (1988; Zbl 0657.62121)] elementary binomial risk model. In order to obtain good results, rather fine discretizations may be necessary and then the computing times may be much too long. Here we show how rather rough discretizations provide approximations of excellent quality when a new claimsize distribution (with one negative probability mass!!!) is adopted and when a new security loading is introduced.

MSC:
62P05 Applications of statistics to actuarial sciences and financial mathematics
60K05 Renewal theory
91B30 Risk theory, insurance (MSC2010)
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References:
[1] De Vylder F., IME 7 pp 1– (1988)
[2] Feller W., An Introduction to Probability Theory and Its Applications (1966) · Zbl 0138.10207
[3] Gerber H., IME 7 pp 15– (1988)
[4] Wikstad N., Astin Bulletin 6 pp 147– (1971)
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