zbMATH — the first resource for mathematics

Estimation of ruin probabilities by means of hazard rates. (English) Zbl 0686.62093
Summary: We show that the asymptotic behaviour of the hazard rate of the claim- size distribution determines not only the singular point of the moment generating function but can also be used to estimate the asymptotic ruin probability. We shall use these results to classify the relevant claim- size distributions and calculate the respective ruin probabilities. Hereby we shall concentrate on the case where Cramér’s method does not work.

62P05 Applications of statistics to actuarial sciences and financial mathematics
62E20 Asymptotic distribution theory in statistics
Full Text: DOI
[1] Beard, R.E.; Pentikäinen, T.; Pesonen, E., ()
[2] Bingham, N.H.; Goldie, C.M.; Teugels, J.L., Regular variation, (1987), Cambridge University Press Cambridge
[3] Embrechts, P., A property of the generalized inverse Gaussian distribution with some applications, J. appl. prob., 20, 537-544, (1983) · Zbl 0536.60022
[4] Embrechts, P.; Veraverbeke, N., Estimates of the probability of ruin with special emphasis on the possibility of large claims, Insurance: math. and econom., 1, 55-72, (1982) · Zbl 0518.62083
[5] Embrechts, P.; Villasenor, J.A., Ruin estimates for large claims, Insurance: math. and econom., 7, 269-274, (1988) · Zbl 0666.62098
[6] Gerber, H.U., An introduction to mathematical risk theory, 8, (1979), Irwin Homewood, IL, Hübner Foundation Monograph · Zbl 0431.62066
[7] Klüppelberg, C., Subexponentielle verteilungen und charakterisierungen verwandter klassen, Dissertation, (1987), University of Mannheim Mannheim · Zbl 0631.62016
[8] Klüppelberg, C., Subexponential distributions and integrated tails, J. appl. prob., 25, 132-141, (1988) · Zbl 0651.60020
[9] Klüppelberg, C., Subexponential distributions and characterizations of related classes, Prob. th. rel. fields, 82, 259-269, (1989) · Zbl 0687.60017
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.