# zbMATH — the first resource for mathematics

Bounds for classical ruin probabilities. (English) Zbl 0547.62068
This paper derives upper and lower bounds for the ruin probability over infinite time. The key observation is that if $$u=k*(1-u),$$ then $$v-u=(v- k*(1-v))*(1-u),$$ where $$(f*g)(x)=\int^{x}_{0}f(x-y)dg(y)$$. Applications to sub-exponential distributions are also given.
Reviewer: E.Shiu

##### MSC:
 62P05 Applications of statistics to actuarial sciences and financial mathematics
Full Text:
##### References:
 [1] Athreya, K.B.; Ney, P., Branching processes, (1972), Springer Berlin-Heidelberg-New York · Zbl 0259.60002 [2] Chistyakov, V.P., A theorem on sums of independent random variables and its applications to branching processes, Theor. probab. appl., 9, 640-648, (1964) · Zbl 0203.19401 [3] Embrechts, P.; Goldie, C.M.; Veraverbeke, N., Subexponentially and infinite divisibility, Z. wahrsch. verw. geb., 49, 335-347, (1979) · Zbl 0397.60024 [4] Embrechts, P.; Veraverbeke, N., Estimates for the probability of ruin with special emphasis on the possibility of large claims, Insurance math. econom., 1, 1, 55-72, (1982) · Zbl 0518.62083 [5] Taylor, G.C., Use of differential and integral inequalities to bound ruin and queuing probabilities, Scand. actuarial J., 197-208, (1976) · Zbl 0338.60005 [6] Teugels, J.L., The class of subexponential distributions, Ann. probab., 3, 1000-1011, (1975) · Zbl 0374.60022 [7] Veraverbeke, N., Asymptotic behaviour of Wiener-Hopf factors of a random walk, Stochastic process. appl., 5, 27-37, (1977) · Zbl 0353.60073
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.