zbMATH — the first resource for mathematics

The probability of ruin for the inverse Gaussian and related processes. (English) Zbl 0768.62097
Summary: We consider a family of aggregate claims processes that contains the gamma process, the inverse Gaussian process, and the compound Poisson process with gamma or degenerate claim amount distribution as special cases. This is a one-parameter family of stochastic processes. It is shown how the probability of ruin can be calculated for this family. Extensive numerical results are given and the role of the parameter is discussed.

62P05 Applications of statistics to actuarial sciences and financial mathematics
62Q05 Statistical tables
Full Text: DOI
[1] Abramowitz, M.; Stegun, I.A., Handbook of mathematical functions, (1964), National Bureau of Standards Washington, D.C, Reprinted by Dover, New York · Zbl 0515.33001
[2] Bowers, N.J.; Gerber, H.U.; Hickman, J.C.; Jones, D.A.; Nesbitt, C.J., Actuarial mathematics, (1986), Society of Actuaries Itasca, IL · Zbl 0634.62107
[3] Feller, W., An introduction to probability theory and its applications, 2, (1971), Wiley New York · Zbl 0219.60003
[4] Dufresne, F.; Gerber, H.U., Three methods to calculate the probability of ruin, ASTIN bulletin, 19, 71-90, (1989)
[5] Dufresne, F.; Gerber, H.U.; Shiu, E.S.W., Risk theory with the gamma process, ASTIN bulletin, 21, 177-192, (1991)
[6] Gerber, H.U., On the probability of ruin for infinitely divisible claim amount distributions, Insurance: mathematics and economics, 11, 2, 163-166, (1992) · Zbl 0781.62162
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.