×

zbMATH — the first resource for mathematics

Ruin estimates for large claims. (English) Zbl 0666.62098
The classical Cramér estimate for the probability of ruin in the Cramér-Lundberg model assumes that the claimsizes are exponentially bounded. In the case of large claims (Pareto, log-normal,...) the condition of sub-exponentiality on the integrated claimsize distribution is the relevant one. In this paper, we study a family of distribution functions which is rich enough to contain the most important claimsize models and for which an easily verifiable sufficient condition for sub- exponentiality holds.

MSC:
62P05 Applications of statistics to actuarial sciences and financial mathematics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Barlow, R.E.; Proshan, F., Statistical theory of reliability and life testing, (1975), Holt, Rinehart and Winston New York
[2] Beard, R.E.; Pentikäinen, T.; Pesonen, E., ()
[3] Bingham, N.H.; Goldie, C.M.; Teugels, J.L., Regular variation, (1987), Cambridge University Press Cambridge
[4] De Vylder, F.; Goovaerts, M., Bounds for classical ruin probabilities, Insurance: mathematics and economics 3, 121-131, (1984), no. 2 · Zbl 0547.62068
[5] Embrechts, P., A property of the generalized inverse Gaussian distribution with some applications, Journal of applied probability, 20, 537-544, (1983) · Zbl 0536.60022
[6] Embrechts, P.; Goldie, C.M.; Veraverbeke, N., Subexponentiality and infinite divisibility, Z. wahrsch. verw. geb., 49, 335-347, (1979) · Zbl 0397.60024
[7] Embrechts, P.; Omey, E., A property of long tailed distributions, Journal of applied probability, 21, 80-87, (1984) · Zbl 0534.60015
[8] Embrechts, P.; Veraverbeke, N., Estimates of the probability of ruin with special emphasis on the probability of large claims, Insurance: mathematics and economics, 1, 1, 55-72, (1982) · Zbl 0518.62083
[9] Klüppelberg, C., Subexponential distributions and integrated tails, Journal of applied probability, (1988), forthcoming · Zbl 0651.60020
[10] Klüppelberg, C., Asymptotic ruin probabilities and hazard rates, Tech. report., (1988), Universität Mannheim
[11] Pitman, E.J.G., Subexponential distribution functions, J. austral. math. soc., A29, 337-347, (1980) · Zbl 0425.60012
[12] Stromberg, K.R., An introduction to classical real analysis, (1981), Wadsworth, Inc Belmont, CA · Zbl 0454.26001
[13] Teugels, J.L., The class of subexponential distributions, The annals of probability, 3, 1001-1011, (1975) · Zbl 0374.60022
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.