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When does the surplus reach a given target? (English) Zbl 0731.62153
Summary: In the classical model of risk theory a martingale method is used to compute the distributions of the first and last passage times (and of their difference) of the surplus process at a given level. As a byproduct a certain probabilistic identity related to Lagrange’s formula is derived; furthermore, P. C. Consul’s [Generalized Poisson distributions. Properties and applications (1989; Zbl 0691.62015)] generalized Poisson distribution is explained.

MSC:
62P05 Applications of statistics to actuarial sciences and financial mathematics
60G99 Stochastic processes
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References:
[1] Consul, P.C., Generalized Poisson distributions: properties and applications, (1989), Marcel Dekker Inc New York, Basel · Zbl 0691.62015
[2] Consul, P.C., A model for distributions of injuries in auto-accidents, Bulletin of the swiss association of actuaries, (1990)
[3] Consul, P.C.; Jain, G.C., A generalization of Poisson distribution, Technometrics, 15, 791-799, (1973) · Zbl 0271.60020
[4] Dufresne, F.; Gerber, H.U., The surpluses immediately before and at ruin, and the amount of the claim causing ruin, Insurance: mathematics & economics, 7, 193-199, (1988) · Zbl 0674.62072
[5] Gerber, H.U., Mathematical fun with ruin theory, Insurance: mathematics & economics, 7, 15-23, (1988) · Zbl 0657.62121
[6] Riordan, J.; Riordan, J., Combinatorial identities, (1979), Robert E. Krieger Publishing Company New York, Reprinted
[7] Shiu, E.S.W., Ruin probability by operational calculus, Insurance: mathematics & economics, 8, 243-249, (1989) · Zbl 0687.62089
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