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Ruin estimates under interest force. (English) Zbl 0838.62098
Summary: We discuss infinite time ruin probabilities in continuous time in a compound Poisson process with a constant premium rate and a constant interest rate. We discuss equations for the ruin probability as well as approximations and upper and lower bounds. Two special cases are treated in more detail: the case with zero initial reserve, and the case with exponential claim sizes.

MSC:
62P05 Applications of statistics to actuarial sciences and financial mathematics
45H05 Integral equations with miscellaneous special kernels
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[1] Asmussen, S., Applied probability and queues, (1987), Wiley New York · Zbl 0624.60098
[2] Beard, R.E.; Pentikainen, T.; Pesonen, E., Risk theory, (1984), Chapman & Hall London · Zbl 0532.62081
[3] Beekman, J.A., Two stochastic processes, (1974), Almqvist and Wiksell Stockholm · Zbl 0137.35601
[4] Boogaert, P.; Crijns, V., Upper bounds on ruin probabilities in case of negative loadings and positive interest rates, Insurance: mathematics and economics, 6, 221-232, (1987) · Zbl 0642.62058
[5] Boogaert, P.; Haezendonck, J.; Delbaen, F., Limit theorems for the present value of the surplus of an insurance portfolio, Insurance: mathematics and economics, 7, 131-138, (1988) · Zbl 0683.62059
[6] Bühlmann, J., Mathematical methods in risk theory, (1970), Springer Verlag Heidelberg · Zbl 0209.23302
[7] Delbaen, F.; Haezendonck, J., Classical risk theory in an economic environment, Insurance: mathematics and econimics, 6, 85-116, (1987) · Zbl 0622.62098
[8] Embrechts, P.; Jensen, J.L.; Maejima, M.; Teugels, J.L., Approximations for compound Poisson and Pólya processes, Advances in applied probability, 17, 623-637, (1985) · Zbl 0576.62098
[9] Feller, W., ()
[10] Gerber, H.U., Der einfluss von zins auf die ruinwahrscheinlichkeit, Mitteilungen vereinigung schweizerische versicherungsmathematiker, 71, 63-70, (1971) · Zbl 0217.26804
[11] Gerber, H.U., The discounted central limit theorem and its Berry-esséen analogue, Annals of mathematical statistics, 42, 389-392, (1971) · Zbl 0224.60012
[12] Gerber, H.U., An introduction to mathematical risk theory, (1979), University of Pennsylvania Philadelphia, PA, SS. Huebner Foundation for Insurance Education · Zbl 0431.62066
[13] Gradshteyn, I.S.; Ryzhik, I.M., ()
[14] Harrison, J.M., Ruin problems with compounding assets, Stochastic processes appl., 5, 67-79, (1977) · Zbl 0361.60053
[15] Mitrinovic, D.S., Analytic inequalities, (1970), Springer Verlag Berlin · Zbl 0199.38101
[16] Ross, S.S., Stochastic processes, (1988), J. Wiley New York
[17] Segerdahl, C.O., Über einige risikotheoretische fragestellungen, Skand. aktuaritidskrift, 61, 43-83, (1942) · Zbl 0026.41901
[18] Segerdahl, C.O., A survey of results in the collective theory of risk, (), 276-299 · Zbl 0122.15501
[19] Sundt, B., An introduction to non-life insurance mathematics, (1993), Verlag Versicherungswissenschaft Karlsruhe · Zbl 0811.62098
[20] Sundt, B.; Teugels, J.L., The adjustment function in ruin estimates under interest force, (1994) · Zbl 0910.62107
[21] Teugels, J.L., Approximation and estimation of some compound distributions, Insurance: mathematics and economics, 4, 143-153, (1985) · Zbl 0583.62091
[22] Teugels, J.L.; Willmot, G., Approximations for stop-loss premiums, Insurance: mathematics and economics, 6, 195-202, (1987) · Zbl 0624.62097
[23] Widder, D., The Laplace transform, (1946), Princeton University Press Princeton, NJ · JFM 67.0384.01
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