# zbMATH — the first resource for mathematics

The probability and severity of ruin for combinations of exponential claim amount distributions and their translations. (English) Zbl 0637.62101
In the classical compound Poisson model of the collective risk theory let $$\psi$$ (u,y) denote the probability that ruin occurs and that the negative surplus at the time of ruin is less than -y. It is shown how this function, which also measures the severity of ruin, can be calculated if the claim amount distribution is a translation of a combination of exponential distributions. Furthermore, these results can be applied to a certain discrete time model.

##### MSC:
 62P05 Applications of statistics to actuarial sciences and financial mathematics 62E15 Exact distribution theory in statistics
Full Text:
##### References:
 [1] Bowers, N.L.; Gerber, H.U.; Hickman, J.C.; Jones, D.A.; Nesbitt, C.J., Actuarial mathematics, (1987), Society of Actuaries Itasca, IL [2] Dufresne, F.; Gerber, H.U., Three methods to calculate the probability of ruin, (1987), Paper submitted for publication · Zbl 0768.62097 [3] Evgrafov, M.A., Analytic functions, (1978), Dover New York · Zbl 0395.30002 [4] Gerber, H.U.; Goovaerts, M.J.; Kaas, R., On the probability and severity of ruin, Astin bulletin, 17, 151-163, (1987) [5] Gerber, H.U., The dilemma between dividends and safety and a generalization of the lundberg—cramér formulas, Scandinavian actuarial journal, 46-57, (1974) · Zbl 0281.62097 [6] Marsden, J.E.; Hoffman, M.J., Basic complex analysis, (1987), Freeman New York · Zbl 0644.30001
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.